diff --git a/pyomo/core/base/block.py b/pyomo/core/base/block.py
index a0948c693d7..2918ef78b00 100644
--- a/pyomo/core/base/block.py
+++ b/pyomo/core/base/block.py
@@ -9,6 +9,7 @@
 #  This software is distributed under the 3-clause BSD License.
 #  ___________________________________________________________________________
 
+from __future__ import annotations
 import copy
 import logging
 import sys
@@ -21,6 +22,7 @@
 from io import StringIO
 from itertools import filterfalse, chain
 from operator import itemgetter, attrgetter
+from typing import Union, Any, Type
 
 from pyomo.common.autoslots import AutoSlots
 from pyomo.common.collections import Mapping
@@ -44,6 +46,7 @@
 from pyomo.core.base.indexed_component import (
     ActiveIndexedComponent,
     UnindexedComponent_set,
+    IndexedComponent,
 )
 
 from pyomo.opt.base import ProblemFormat, guess_format
@@ -539,7 +542,7 @@ def __init__(self, component):
         super(_BlockData, self).__setattr__('_decl_order', [])
         self._private_data = None
 
-    def __getattr__(self, val):
+    def __getattr__(self, val) -> Union[Component, IndexedComponent, Any]:
         if val in ModelComponentFactory:
             return _component_decorator(self, ModelComponentFactory.get_class(val))
         # Since the base classes don't support getattr, we can just
@@ -548,7 +551,7 @@ def __getattr__(self, val):
             "'%s' object has no attribute '%s'" % (self.__class__.__name__, val)
         )
 
-    def __setattr__(self, name, val):
+    def __setattr__(self, name: str, val: Union[Component, IndexedComponent, Any]):
         """
         Set an attribute of a block data object.
         """
@@ -2007,6 +2010,17 @@ class Block(ActiveIndexedComponent):
     _ComponentDataClass = _BlockData
     _private_data_initializers = defaultdict(lambda: dict)
 
+    @overload
+    def __new__(
+        cls: Type[Block], *args, **kwds
+    ) -> Union[ScalarBlock, IndexedBlock]: ...
+
+    @overload
+    def __new__(cls: Type[ScalarBlock], *args, **kwds) -> ScalarBlock: ...
+
+    @overload
+    def __new__(cls: Type[IndexedBlock], *args, **kwds) -> IndexedBlock: ...
+
     def __new__(cls, *args, **kwds):
         if cls != Block:
             return super(Block, cls).__new__(cls)
@@ -2251,6 +2265,11 @@ class IndexedBlock(Block):
     def __init__(self, *args, **kwds):
         Block.__init__(self, *args, **kwds)
 
+    @overload
+    def __getitem__(self, index) -> _BlockData: ...
+
+    __getitem__ = IndexedComponent.__getitem__  # type: ignore
+
 
 #
 # Deprecated functions.
diff --git a/pyomo/core/base/constraint.py b/pyomo/core/base/constraint.py
index 8cf3c48ad0a..fde1160e563 100644
--- a/pyomo/core/base/constraint.py
+++ b/pyomo/core/base/constraint.py
@@ -9,10 +9,12 @@
 #  This software is distributed under the 3-clause BSD License.
 #  ___________________________________________________________________________
 
+from __future__ import annotations
 import sys
 import logging
 from weakref import ref as weakref_ref
 from pyomo.common.pyomo_typing import overload
+from typing import Union, Type
 
 from pyomo.common.deprecation import RenamedClass
 from pyomo.common.errors import DeveloperError
@@ -42,6 +44,7 @@
     ActiveIndexedComponent,
     UnindexedComponent_set,
     rule_wrapper,
+    IndexedComponent,
 )
 from pyomo.core.base.set import Set
 from pyomo.core.base.disable_methods import disable_methods
@@ -728,6 +731,17 @@ class Infeasible(object):
     Violated = Infeasible
     Satisfied = Feasible
 
+    @overload
+    def __new__(
+        cls: Type[Constraint], *args, **kwds
+    ) -> Union[ScalarConstraint, IndexedConstraint]: ...
+
+    @overload
+    def __new__(cls: Type[ScalarConstraint], *args, **kwds) -> ScalarConstraint: ...
+
+    @overload
+    def __new__(cls: Type[IndexedConstraint], *args, **kwds) -> IndexedConstraint: ...
+
     def __new__(cls, *args, **kwds):
         if cls != Constraint:
             return super(Constraint, cls).__new__(cls)
@@ -1020,6 +1034,11 @@ def add(self, index, expr):
         """Add a constraint with a given index."""
         return self.__setitem__(index, expr)
 
+    @overload
+    def __getitem__(self, index) -> _GeneralConstraintData: ...
+
+    __getitem__ = IndexedComponent.__getitem__  # type: ignore
+
 
 @ModelComponentFactory.register("A list of constraint expressions.")
 class ConstraintList(IndexedConstraint):
diff --git a/pyomo/core/base/indexed_component.py b/pyomo/core/base/indexed_component.py
index 0d498da091d..e1be613d666 100644
--- a/pyomo/core/base/indexed_component.py
+++ b/pyomo/core/base/indexed_component.py
@@ -18,7 +18,7 @@
 import pyomo.core.base as BASE
 from pyomo.core.base.indexed_component_slice import IndexedComponent_slice
 from pyomo.core.base.initializer import Initializer
-from pyomo.core.base.component import Component, ActiveComponent
+from pyomo.core.base.component import Component, ActiveComponent, ComponentData
 from pyomo.core.base.config import PyomoOptions
 from pyomo.core.base.enums import SortComponents
 from pyomo.core.base.global_set import UnindexedComponent_set
@@ -606,7 +606,7 @@ def iteritems(self):
         """Return a list (index,data) tuples from the dictionary"""
         return self.items()
 
-    def __getitem__(self, index):
+    def __getitem__(self, index) -> ComponentData:
         """
         This method returns the data corresponding to the given index.
         """
diff --git a/pyomo/core/base/param.py b/pyomo/core/base/param.py
index 3ef33b9ee45..5fcaf92b25a 100644
--- a/pyomo/core/base/param.py
+++ b/pyomo/core/base/param.py
@@ -9,11 +9,13 @@
 #  This software is distributed under the 3-clause BSD License.
 #  ___________________________________________________________________________
 
+from __future__ import annotations
 import sys
 import types
 import logging
 from weakref import ref as weakref_ref
 from pyomo.common.pyomo_typing import overload
+from typing import Union, Type
 
 from pyomo.common.autoslots import AutoSlots
 from pyomo.common.deprecation import deprecation_warning, RenamedClass
@@ -291,6 +293,17 @@ class NoValue(object):
 
         pass
 
+    @overload
+    def __new__(
+        cls: Type[Param], *args, **kwds
+    ) -> Union[ScalarParam, IndexedParam]: ...
+
+    @overload
+    def __new__(cls: Type[ScalarParam], *args, **kwds) -> ScalarParam: ...
+
+    @overload
+    def __new__(cls: Type[IndexedParam], *args, **kwds) -> IndexedParam: ...
+
     def __new__(cls, *args, **kwds):
         if cls != Param:
             return super(Param, cls).__new__(cls)
@@ -983,7 +996,7 @@ def _create_objects_for_deepcopy(self, memo, component_list):
     # between potentially variable GetItemExpression objects and
     # "constant" GetItemExpression objects.  That will need to wait for
     # the expression rework [JDS; Nov 22].
-    def __getitem__(self, args):
+    def __getitem__(self, args) -> _ParamData:
         try:
             return super().__getitem__(args)
         except:
diff --git a/pyomo/core/base/set.py b/pyomo/core/base/set.py
index 2dc14460911..b3277ab3260 100644
--- a/pyomo/core/base/set.py
+++ b/pyomo/core/base/set.py
@@ -9,6 +9,7 @@
 #  This software is distributed under the 3-clause BSD License.
 #  ___________________________________________________________________________
 
+from __future__ import annotations
 import inspect
 import itertools
 import logging
@@ -16,6 +17,8 @@
 import sys
 import weakref
 from pyomo.common.pyomo_typing import overload
+from typing import Union, Type, Any as typingAny
+from collections.abc import Iterator
 
 from pyomo.common.collections import ComponentSet
 from pyomo.common.deprecation import deprecated, deprecation_warning, RenamedClass
@@ -569,7 +572,7 @@ def isordered(self):
     def subsets(self, expand_all_set_operators=None):
         return iter((self,))
 
-    def __iter__(self):
+    def __iter__(self) -> Iterator[typingAny]:
         """Iterate over the set members
 
         Raises AttributeError for non-finite sets.  This must be
@@ -1967,6 +1970,12 @@ class SortedOrder(object):
     _ValidOrderedAuguments = {True, False, InsertionOrder, SortedOrder}
     _UnorderedInitializers = {set}
 
+    @overload
+    def __new__(cls: Type[Set], *args, **kwds) -> Union[_SetData, IndexedSet]: ...
+
+    @overload
+    def __new__(cls: Type[OrderedScalarSet], *args, **kwds) -> OrderedScalarSet: ...
+
     def __new__(cls, *args, **kwds):
         if cls is not Set:
             return super(Set, cls).__new__(cls)
@@ -2373,6 +2382,11 @@ def data(self):
         "Return a dict containing the data() of each Set in this IndexedSet"
         return {k: v.data() for k, v in self.items()}
 
+    @overload
+    def __getitem__(self, index) -> _SetData: ...
+
+    __getitem__ = IndexedComponent.__getitem__  # type: ignore
+
 
 class FiniteScalarSet(_FiniteSetData, Set):
     def __init__(self, **kwds):
diff --git a/pyomo/core/base/var.py b/pyomo/core/base/var.py
index f426c9c4f55..856a2dc0237 100644
--- a/pyomo/core/base/var.py
+++ b/pyomo/core/base/var.py
@@ -9,10 +9,12 @@
 #  This software is distributed under the 3-clause BSD License.
 #  ___________________________________________________________________________
 
+from __future__ import annotations
 import logging
 import sys
 from pyomo.common.pyomo_typing import overload
 from weakref import ref as weakref_ref
+from typing import Union, Type
 
 from pyomo.common.deprecation import RenamedClass
 from pyomo.common.log import is_debug_set
@@ -668,6 +670,15 @@ class Var(IndexedComponent, IndexedComponent_NDArrayMixin):
 
     _ComponentDataClass = _GeneralVarData
 
+    @overload
+    def __new__(cls: Type[Var], *args, **kwargs) -> Union[ScalarVar, IndexedVar]: ...
+
+    @overload
+    def __new__(cls: Type[ScalarVar], *args, **kwargs) -> ScalarVar: ...
+
+    @overload
+    def __new__(cls: Type[IndexedVar], *args, **kwargs) -> IndexedVar: ...
+
     def __new__(cls, *args, **kwargs):
         if cls is not Var:
             return super(Var, cls).__new__(cls)
@@ -688,7 +699,7 @@ def __init__(
         dense=True,
         units=None,
         name=None,
-        doc=None
+        doc=None,
     ): ...
 
     def __init__(self, *args, **kwargs):
@@ -1046,7 +1057,7 @@ def domain(self, domain):
     # between potentially variable GetItemExpression objects and
     # "constant" GetItemExpression objects.  That will need to wait for
     # the expression rework [JDS; Nov 22].
-    def __getitem__(self, args):
+    def __getitem__(self, args) -> _GeneralVarData:
         try:
             return super().__getitem__(args)
         except RuntimeError: