diff --git a/parse_magic.py b/parse_magic.py
index 8e0bb76..840739a 100644
--- a/parse_magic.py
+++ b/parse_magic.py
@@ -4,6 +4,7 @@ Parses the Magic Ugly Data File Format
 Assumes the base logic is R with no extra connectives
 """
 import argparse
+import re
 import sys
 from typing import TextIO, List, Optional, Tuple, Set, Dict
 
@@ -23,14 +24,31 @@ class SourceFile:
         self.current_line = 0
         self.reststr = ""
 
-    def __next__(self):
+    def next_line(self):
         if self.reststr != "":
-            return self.reststr
+            reststr = self.reststr
+            self.reststr = ""
+            return reststr
 
-        contents = next(self.fileobj)
+        contents = next(self.fileobj).strip()
         self.current_line += 1
         return contents
 
+    def __next__(self):
+        """
+        Grabs the next word token from the stream
+        """
+        if self.reststr == "":
+            self.reststr = next(self.fileobj).strip()
+            self.current_line += 1
+
+        tokens = self.reststr.split(" ")
+        next_token = tokens[0]
+        self.reststr = " ".join(tokens[1:])
+
+        return next_token
+
+
     def set_reststr(self, reststr: str):
         self.reststr = reststr
 
@@ -44,49 +62,95 @@ class ModelBuilder:
     def __init__(self):
         self.size : int = 0
         self.carrier_set : Set[ModelValue] = set()
-        self.num_negation: int = 0
         self.mnegation: Optional[ModelFunction] = None
-        self.num_order: int = 0
         self.mconjunction: Optional[ModelFunction] = None
         self.mdisjunction: Optional[ModelFunction] = None
-        self.num_designated: int = 0
         self.designated_values: Set[ModelValue] = set()
-        self.num_implication: int = 0
         self.mimplication: Optional[ModelFunction] = None
-        self.num_necessitation: int = 0
         self.mnecessitation: Optional[ModelFunction] = None
-        self.custom_model_functions: List[Tuple[int, ModelFunction]]
+        self.custom_model_functions: Dict[str,  ModelFunction] = {}
 
 class Stage:
     def __init__(self, name: str):
         self.name = name
         self.next: Optional['Stage'] = None
         self.previous: Optional['Stage'] = None
+        self.num = 0
+
+    def increment(self):
+        self.num += 1
+
+    def reset(self):
+        self.num = 0
+
     def __str__(self):
         return self.name
 
 class Stages:
     def __init__(self):
         self.stages: Dict[str, Stage] = {}
-        self.last_stage: Optional[Stage] = None
+        self.last_added_stage: Optional[Stage] = None
+        self.first_stage: Optional[Stage] = None
+
     def add(self, name: str):
         stage = Stage(name)
         stage.next = stage
-        if self.last_stage is not None:
-            stage.previous = self.last_stage
-            self.last_stage.next = stage
+
+        if self.last_added_stage is not None:
+            stage.previous = self.last_added_stage
+            self.last_added_stage.next = stage
         else:
+            # The previous of the first stage
+            # is the end
+            self.first_stage = stage
             stage.previous = Stage("end")
 
         self.stages[name] = stage
-        self.last_stage = stage
+        self.last_added_stage = stage
+
     def next_stage(self, name):
         return self.stages[name].next
+
     def previous_stage(self, name):
         return self.stages[name].previous
+
+    def reset_after(self, name):
+        stage = self.stages[name]
+        stage.reset()
+        if stage.next.name == "process_model":
+            return
+        next_stage = stage.next
+        while next_stage is not None:
+            next_stage.reset()
+            if next_stage.next.name == "process_model":
+                next_stage = None
+            else:
+                next_stage = next_stage.next
+
     def get(self, name):
         return self.stages[name]
 
+    def name(self):
+        result = ""
+        stage = self.first_stage
+        if stage is None:
+            return ""
+
+        result = f"{stage.num}"
+        if stage.next == "process_model":
+            return result
+
+        stage = stage.next
+        while stage is not None:
+            result += f".{stage.num}"
+            if stage.next.name != "process_model":
+                stage = stage.next
+            else:
+                stage = None
+
+        return result
+
+
 def derive_stages(header: UglyHeader) -> Stages:
     stages = Stages()
     stages.add("size")
@@ -97,9 +161,8 @@ def derive_stages(header: UglyHeader) -> Stages:
     stages.add("implication")
     if header.necessitation:
         stages.add("necessitation")
-    # TODO: Can't use -- as that can be a custom symbol
-    # for (acidity, symbol) in header.custom_model_functions:
-        # stages.add(f"custom--{acidity}--{symbol}")
+    for (adicity, symbol) in header.custom_model_functions:
+        stages.add(f"custom--{adicity}--{symbol}")
     stages.add("process_model")
 
     # After processing the model, go to the previous stage
@@ -107,7 +170,6 @@ def derive_stages(header: UglyHeader) -> Stages:
 
     return stages
 
-
 def parse_matrices(infile: SourceFile) -> List[Tuple[Model, Dict]]:
     solutions = [] # Reset
     header = parse_header(infile)
@@ -116,34 +178,85 @@ def parse_matrices(infile: SourceFile) -> List[Tuple[Model, Dict]]:
     current_model_parts = ModelBuilder()
     stage = stages.get("size")
     while True:
-        print("Current stage:", stage)
         match stage.name:
             case "end":
                 break
             case "process_model":
-                process_model(current_model_parts, solutions)
+                process_model(stages.name(), current_model_parts, solutions)
                 stage = stage.next
             case "size":
                 processed = process_sizes(infile, current_model_parts, first_run)
                 first_run = False
-                stage = stage.next if processed else stage.previous
+                if processed:
+                    stage.num = current_model_parts.size + 1
+                    stage = stage.next
+                else:
+                    stages.reset_after(stage.name)
+                    stage = stage.previous
             case "negation":
                 processed = process_negations(infile, current_model_parts)
-                stage = stage.next if processed else stage.previous
+                if processed:
+                    stage.increment()
+                    stage = stage.next
+                else:
+                    stages.reset_after(stage.name)
+                    stage = stage.previous
             case "order":
                 processed = process_orders(infile, current_model_parts)
-                stage = stage.next if processed else stage.previous
+                if processed:
+                    stage.increment()
+                    stage = stage.next
+                else:
+                    stages.reset_after(stage.name)
+                    stage = stage.previous
             case "designated":
                 processed = process_designateds(infile, current_model_parts)
-                stage = stage.next if processed else stage.previous
+                if processed:
+                    stage.increment()
+                    stage = stage.next
+                else:
+                    stages.reset_after(stage.name)
+                    stage = stage.previous
             case "implication":
                 processed = process_implications(infile, current_model_parts)
-                stage = stage.next if processed else stage.previous
+                if processed:
+                    stage.increment()
+                    stage = stage.next
+                else:
+                    stages.reset_after(stage.name)
+                    stage = stage.previous
             case "necessitation":
                 processed = process_necessitations(infile, current_model_parts)
-                stage = stage.next if processed else stage.previous
+                if processed:
+                    stage.increment()
+                    stage = stage.next
+                else:
+                    stages.reset_after(stage.name)
+                    stage = stage.previous
             case _:
-                raise NotImplementedError("Custom Connectives are not yet supported")
+                custom_stage = re.search(r"custom--(\d+)--(\S+)", stage.name)
+                if custom_stage is None or len(custom_stage.groups()) != 2:
+                    raise NotImplementedError(f"Unrecognized Stage: {stage.name}")
+                adicity, symbol = custom_stage.groups()
+                adicity = int(adicity)
+                processed = True
+                if adicity == 0:
+                    # We don't need to do anything here
+                    stage = stage.next
+                elif adicity == 1:
+                    processed = process_custom_monadic_connective(infile, symbol, current_model_parts)
+                elif adicity == 2:
+                    processed = process_custom_dyadic_connective(infile, symbol, current_model_parts)
+                else:
+                    raise NotImplementedError("Unable to process connectives of adicity greater than c2")
+
+                if processed:
+                    stage.increment()
+                    stage = stage.next
+                else:
+                    stages.reset_after(stage.name)
+                    stage = stage.previous
+
 
     return solutions
 
@@ -156,15 +269,8 @@ def process_sizes(infile: SourceFile, current_model_parts: ModelBuilder, first_r
         return False
 
     carrier_set = carrier_set_from_size(size)
-    current_model_parts.size = size
     current_model_parts.carrier_set = carrier_set
-
-    # Reset counts
-    current_model_parts.num_negation = 0
-    current_model_parts.num_order = 0
-    current_model_parts.num_designated = 0
-    current_model_parts.num_implication = 0
-    current_model_parts.num_necessitation = 0
+    current_model_parts.size = size
 
     return True
 
@@ -174,15 +280,7 @@ def process_negations(infile: SourceFile, current_model_parts: ModelBuilder) ->
     if mnegation is None:
         return False
 
-    current_model_parts.num_negation += 1
     current_model_parts.mnegation = mnegation
-
-    # Reset counts
-    current_model_parts.num_order = 0
-    current_model_parts.num_designated = 0
-    current_model_parts.num_implication = 0
-    current_model_parts.num_necessitation = 0
-
     return True
 
 def process_orders(infile: SourceFile, current_model_parts: ModelBuilder) -> bool:
@@ -192,15 +290,9 @@ def process_orders(infile: SourceFile, current_model_parts: ModelBuilder) -> boo
         return False
 
     mconjunction, mdisjunction = result
-    current_model_parts.num_order += 1
     current_model_parts.mconjunction = mconjunction
     current_model_parts.mdisjunction = mdisjunction
 
-    # Reset counts
-    current_model_parts.num_designated = 0
-    current_model_parts.num_implication = 0
-    current_model_parts.num_necessitation = 0
-
     return True
 
 def process_designateds(infile: SourceFile, current_model_parts: ModelBuilder) -> bool:
@@ -209,58 +301,48 @@ def process_designateds(infile: SourceFile, current_model_parts: ModelBuilder) -
     if designated_values is None:
         return False
 
-    current_model_parts.num_designated += 1
     current_model_parts.designated_values = designated_values
-
-    # Reset counts
-    current_model_parts.num_implication = 0
-    current_model_parts.num_necessitation = 0
-
     return True
 
 def process_implications(infile: SourceFile, current_model_parts: ModelBuilder) -> bool:
     """Stage 5"""
-    if infile.reststr == "":
-        infile.reststr = next(infile).strip()
-
-    mimplication, reststr = parse_single_implication(infile.reststr, infile.current_line, current_model_parts.size)
-    infile.reststr = reststr
+    mimplication = parse_single_implication(infile, current_model_parts.size)
     if mimplication is None:
         return False
 
-    current_model_parts.num_implication += 1
     current_model_parts.mimplication = mimplication
-
-     # Reset counts
-    current_model_parts.num_necessitation = 0
-
     return True
 
 def process_necessitations(infile: SourceFile, current_model_parts: ModelBuilder) -> bool:
-    # TODO: In progress
-    if infile.reststr != "":
-        infile.reststr = next(infile).strip()
-
-    # TODO: This should match the implication way of doing things when
-    # custom conenctives are involved (returning reststr)
-    mnecessitation, reststr = parse_single_necessitation_from_str(infile.reststr, infile.current_line, current_model_parts.size)
-    infile.reststr = reststr
+    mnecessitation = parse_single_necessitation(infile, current_model_parts.size)
     if mnecessitation is None:
         return False
 
-    current_model_parts.num_necessitation += 1
     current_model_parts.mnecessitation = mnecessitation
-
     return True
 
-def process_model(mp: ModelBuilder, solutions: List[Tuple[Model, Dict]]):
+def process_custom_monadic_connective(infile: SourceFile, symbol: str, current_model_parts: ModelBuilder) -> bool:
+    mfunction = parse_single_monadic_connective(infile, symbol, current_model_parts.size)
+    if mfunction is None:
+        return False
+
+    current_model_parts.custom_model_functions[symbol] = mfunction
+    return True
+
+def process_custom_dyadic_connective(infile: SourceFile, symbol: str, current_model_parts: ModelBuilder) -> bool:
+    mfunction = parse_single_dyadic_connective(infile, symbol, current_model_parts.size)
+    if mfunction is None:
+        return False
+
+    current_model_parts.custom_model_functions[symbol] = mfunction
+    return True
+
+def process_model(model_name: str, mp: ModelBuilder,  solutions: List[Tuple[Model, Dict]]):
     """Create Model"""
     assert mp.mimplication is not None
-    assert len(mp.carrier_set) > 0
     assert mp.size + 1 == len(mp.carrier_set)
 
     logical_operations = { mp.mimplication }
-    model_name = f"{mp.size + 1}{'.' + str(mp.num_negation) if mp.num_negation != 0 else ''}.{mp.num_order}.{mp.num_designated}.{mp.num_implication}{'.' + str(mp.num_necessitation) if mp.num_necessitation != 0 else ''}"
     model = Model(mp.carrier_set, logical_operations, mp.designated_values, name=model_name)
     interpretation = {
         Implication: mp.mimplication
@@ -278,6 +360,12 @@ def process_model(mp: ModelBuilder, solutions: List[Tuple[Model, Dict]]):
         logical_operations.add(mp.mnecessitation)
         interpretation[Necessitation] = mp.mnecessitation
 
+    for custom_mf in mp.custom_model_functions.values():
+        if custom_mf is not None:
+            logical_operations.add(custom_mf)
+            # NOTE: No need to assign interpretation
+            # for VSP check
+
     solutions.append((model, interpretation))
     print(f"Parsed Matrix {model.name}")
 
@@ -285,7 +373,7 @@ def parse_header(infile: SourceFile) -> UglyHeader:
     """
     Parse the header line from the ugly data format.
     """
-    header_line = next(infile).strip()
+    header_line = infile.next_line()
     header_tokens = header_line.split(" ")
     assert header_tokens[0] in ["0", "1"]
     assert header_tokens[6] in ["0", "1"]
@@ -314,12 +402,12 @@ def parse_size(infile: SourceFile, first_run: bool) -> Optional[int]:
     Parse the line representing the matrix size.
     """
 
-    size = int(next(infile))
+    size = int(infile.next_line())
     # HACK: When necessitation and custom connectives are enabled
     # MaGIC may produce -1s at the beginning of the file
     if first_run:
         while size == -1:
-            size = int(next(infile))
+            size = int(infile.next_line())
 
     if size == -1:
         return None
@@ -330,20 +418,7 @@ def parse_single_negation(infile: SourceFile, size: int) -> Optional[ModelFuncti
     """
     Parse the line representing the negation table.
     """
-    line = next(infile).strip()
-    if line == '-1':
-        return None
-
-    row = line.split(" ")
-    assert len(row) == size + 1, f"Negation table doesn't match size at line {infile.current_line}"
-    mapping = {}
-
-    for i, j in zip(range(size + 1), row):
-        x = mvalue_from_index(i)
-        y = parse_mvalue(j)
-        mapping[(x, )] = y
-
-    return ModelFunction(1, mapping, "¬")
+    return parse_single_monadic_connective(infile, "¬", size)
 
 def mvalue_from_index(i: int) -> ModelValue:
     """
@@ -410,7 +485,7 @@ def parse_single_order(infile: SourceFile, size: int) -> Optional[Tuple[ModelFun
     """
     Parse the line representing the ordering table
     """
-    line = next(infile).strip()
+    line = infile.next_line()
     if line == '-1':
         return None
 
@@ -461,7 +536,7 @@ def parse_single_designated(infile: SourceFile, size: int) -> Optional[Set[Model
     """
     Parse the line representing which model values are designated.
     """
-    line = next(infile).strip()
+    line = infile.next_line()
     if line == '-1':
         return None
 
@@ -477,17 +552,49 @@ def parse_single_designated(infile: SourceFile, size: int) -> Optional[Set[Model
 
     return designated_values
 
-def parse_single_implication(instr: str, line: int, size: int) -> Tuple[ModelFunction, str]:
+def parse_single_implication(infile: SourceFile, size: int) -> Tuple[ModelFunction]:
     """
-    Take the current string, parse an implication table from it,
-    and return along with it the remainder of the string
+    Take the current string, parse an implication table from it.
     """
-    if instr == "-1":
-        return None, ""
+    return parse_single_dyadic_connective(infile, "→", size)
 
-    table = instr.split(" ")
+def parse_single_necessitation(infile: SourceFile, size: int) -> Optional[ModelFunction]:
+    """
+    Parse the line representing the necessitation table.
+    """
+    return parse_single_monadic_connective(infile, "!", size)
 
-    assert len(table) >= (size + 1)**2, f"Implication table does not match expected size at line {line}"
+def parse_single_monadic_connective(infile: SourceFile, symbol: str, size: int) -> Optional[ModelFunction]:
+    line = infile.next_line()
+    if line == '-1':
+        return None
+
+    row = line.split(" ")
+    assert len(row) == size + 1, f"{symbol} table doesn't match size at line {infile.current_line}"
+    mapping = {}
+
+    for i, j in zip(range(size + 1), row):
+        x = mvalue_from_index(i)
+        y = parse_mvalue(j)
+        mapping[(x, )] = y
+
+    return ModelFunction(1, mapping, symbol)
+
+def parse_single_dyadic_connective(infile: SourceFile, symbol: str, size: int) -> Optional[ModelFunction]:
+    try:
+        first_token = next(infile)
+        if first_token == "-1":
+            return None
+    except StopIteration:
+        return None
+
+    table = []
+    try:
+        table = [first_token] + [next(infile) for _ in range((size + 1)**2 - 1)]
+    except StopIteration:
+        pass
+
+    assert len(table) == (size + 1)**2, f"{symbol} table does not match expected size at line {infile.current_line}"
 
     mapping = {}
     table_i = 0
@@ -501,30 +608,7 @@ def parse_single_implication(instr: str, line: int, size: int) -> Tuple[ModelFun
 
             mapping[(x, y)] = r
 
-    mimplication = ModelFunction(2, mapping, "→")
-    reststr = " ".join(table[(size + 1)**2:])
-    return mimplication, reststr
-
-def parse_single_necessitation_from_str(instr: str, line: int, size: int) -> Optional[ModelFunction]:
-    """
-    Parse the line representing the necessitation table.
-    """
-    if instr == "-1":
-        return None
-
-    row = instr.split(" ")
-    assert len(row) >= size + 1, f"Necessitation table doesn't match size at line {line}"
-    mapping = {}
-
-    for i, j in zip(range(size + 1), row):
-        x = mvalue_from_index(i)
-        y = parse_mvalue(j)
-        mapping[(x, )] = y
-
-    mnecessitation = ModelFunction(1, mapping, "!")
-    reststr = " ".join(row[(size + 1):])
-
-    return mnecessitation, reststr
+    return ModelFunction(2, mapping, symbol)
 
 
 if __name__ == "__main__":