diff --git a/pyomo/gdp/plugins/gdp_to_mip_transformation.py b/pyomo/gdp/plugins/gdp_to_mip_transformation.py
index 8dcd22b292a..bc2ed2ad1ba 100644
--- a/pyomo/gdp/plugins/gdp_to_mip_transformation.py
+++ b/pyomo/gdp/plugins/gdp_to_mip_transformation.py
@@ -13,11 +13,13 @@
 
 from pyomo.common.autoslots import AutoSlots
 from pyomo.common.collections import ComponentMap, DefaultComponentMap
+from pyomo.common.config import ConfigDict, ConfigValue
 from pyomo.common.log import is_debug_set
 from pyomo.common.modeling import unique_component_name
 
 from pyomo.core.base import Transformation, TransformationFactory
 from pyomo.core.base.external import ExternalFunction
+from pyomo.core.util import target_list
 from pyomo.core import (
     Any,
     Block,
@@ -64,6 +66,34 @@ class GDP_to_MIP_Transformation(Transformation):
     """
     Base class for transformations from GDP to MIP
     """
+    CONFIG = ConfigDict()
+    CONFIG.declare(
+        'targets',
+        ConfigValue(
+            default=None,
+            domain=target_list,
+            description="target or list of targets that will be relaxed",
+            doc="""
+
+        This specifies the target or list of targets to relax as either a
+        component or a list of components. If None (default), the entire model
+        is transformed. Note that if the transformation is done out of place,
+        the list of targets should be attached to the model before it is cloned,
+        and the list will specify the targets on the cloned instance.""",
+        ),
+    )
+    CONFIG.declare(
+        'one_indicator_for_two_term',
+        ConfigValue(
+            default=False,
+            domain=bool,
+            description="Whether or not to reduce to one indicator binary variable "
+            "in the transformed model for two-term Disjunctions",
+            doc="""
+            TODO
+            """
+        ),
+    )
 
     def __init__(self, logger):
         """Initialize transformation object."""
@@ -102,10 +132,12 @@ def __init__(self, logger):
         self._generate_debug_messages = False
         self._transformation_blocks = {}
         self._algebraic_constraints = {}
+        self._indicator_var_expr = {}
 
     def _restore_state(self):
         self._transformation_blocks.clear()
         self._algebraic_constraints.clear()
+        self._indicator_var_expr = {}
         if hasattr(self, '_config'):
             del self._config
 
@@ -121,6 +153,11 @@ def _process_arguments(self, instance, **kwds):
         self._config.set_value(kwds)
         self._generate_debug_messages = is_debug_set(self.logger)
 
+    def _get_indicator_var(self, disjunct):
+        if disjunct in self._indicator_var_expr:
+            return self._indicator_var_expr[disjunct]
+        return disjunct.binary_indicator_var
+
     def _transform_logical_constraints(self, instance, targets):
         # transform any logical constraints that might be anywhere on the stuff
         # we're about to transform. We do this before we preprocess targets
diff --git a/pyomo/gdp/plugins/hull.py b/pyomo/gdp/plugins/hull.py
index 854366c0cf0..bcf995a93d8 100644
--- a/pyomo/gdp/plugins/hull.py
+++ b/pyomo/gdp/plugins/hull.py
@@ -50,7 +50,6 @@
     is_child_of,
     _warn_for_active_disjunct,
 )
-from pyomo.core.util import target_list
 from pyomo.util.vars_from_expressions import get_vars_from_components
 from weakref import ref as weakref_ref
 
@@ -108,22 +107,7 @@ class Hull_Reformulation(GDP_to_MIP_Transformation):
     corresponding OR or XOR constraint.
     """
 
-    CONFIG = cfg.ConfigDict('gdp.hull')
-    CONFIG.declare(
-        'targets',
-        cfg.ConfigValue(
-            default=None,
-            domain=target_list,
-            description="target or list of targets that will be relaxed",
-            doc="""
-
-        This specifies the target or list of targets to relax as either a
-        component or a list of components. If None (default), the entire model
-        is transformed. Note that if the transformation is done out of place,
-        the list of targets should be attached to the model before it is cloned,
-        and the list will specify the targets on the cloned instance.""",
-        ),
-    )
+    CONFIG = GDP_to_MIP_Transformation.CONFIG()
     CONFIG.declare(
         'perspective function',
         cfg.ConfigValue(
@@ -309,6 +293,12 @@ def _transform_disjunctionData(
         # change their active status when we transform them, but we still need
         # this list after the fact.
         active_disjuncts = [disj for disj in obj.disjuncts if disj.active]
+        two_term = False
+        if self._config.one_indicator_for_two_term and len(active_disjuncts) == 2:
+            two_term = True
+            binary = active_disjuncts[0].binary_indicator_var
+            self._indicator_var_expr[active_disjuncts[0]] = binary
+            self._indicator_var_expr[active_disjuncts[1]] = 1 - binary
 
         # We put *all* transformed things on the parent Block of this
         # disjunction. We'll mark the disaggregated Vars as local, but beyond
@@ -405,7 +395,7 @@ def _transform_disjunctionData(
         parent_local_var_list = self._get_local_var_list(parent_disjunct)
         or_expr = 0
         for disjunct in obj.disjuncts:
-            or_expr += disjunct.indicator_var.get_associated_binary()
+            or_expr += self._get_indicator_var(disjunct)
             if disjunct.active:
                 self._transform_disjunct(
                     obj=disjunct,
@@ -416,10 +406,11 @@ def _transform_disjunctionData(
                     parent_disjunct_local_vars=local_vars_by_disjunct[parent_disjunct],
                     disjunct_disaggregated_var_map=disjunct_disaggregated_var_map,
                 )
-        xorConstraint.add(index, (or_expr, 1))
-        # map the DisjunctionData to its XOR constraint to mark it as
-        # transformed
-        obj._algebraic_constraint = weakref_ref(xorConstraint[index])
+        if not two_term:
+            xorConstraint.add(index, (or_expr, 1))
+            # map the DisjunctionData to its XOR constraint to mark it as
+            # transformed
+            obj._algebraic_constraint = weakref_ref(xorConstraint[index])
 
         # Now add the reaggregation constraints
         for var in all_vars_to_disaggregate:
@@ -439,7 +430,7 @@ def _transform_disjunctionData(
                     parent_local_var_list.append(disaggregated_var)
                 local_vars_by_disjunct[parent_disjunct].add(disaggregated_var)
                 var_free = 1 - sum(
-                    disj.indicator_var.get_associated_binary()
+                    self._get_indicator_var(disj)
                     for disj in disjuncts_var_appears_in[var]
                 )
                 self._declare_disaggregated_var_bounds(
@@ -546,7 +537,7 @@ def _transform_disjunct(
                 bigmConstraint=bigmConstraint,
                 lb_idx='lb',
                 ub_idx='ub',
-                var_free_indicator=obj.indicator_var.get_associated_binary(),
+                var_free_indicator=self._get_indicator_var(obj),
             )
             # update the bigm constraint mappings
             data_dict = disaggregatedVar.parent_block().private_data()
@@ -575,7 +566,7 @@ def _transform_disjunct(
                 bigmConstraint=bigmConstraint,
                 lb_idx='lb',
                 ub_idx='ub',
-                var_free_indicator=obj.indicator_var.get_associated_binary(),
+                var_free_indicator=self._get_indicator_var(obj),
             )
             # update the bigm constraint mappings
             data_dict = var.parent_block().private_data()
@@ -688,7 +679,7 @@ def _transform_constraint(
                     c.body, substitute=zero_substitute_map
                 )
 
-            y = disjunct.binary_indicator_var
+            y = self._get_indicator_var(disjunct)
             if NL:
                 if mode == "LeeGrossmann":
                     sub_expr = clone_without_expression_components(