diff --git a/src/wmtk/invariants/Invariant.cpp b/src/wmtk/invariants/Invariant.cpp
index a14059d84d..dfd951e38b 100644
--- a/src/wmtk/invariants/Invariant.cpp
+++ b/src/wmtk/invariants/Invariant.cpp
@@ -2,6 +2,7 @@
 #include <wmtk/Mesh.hpp>
 #include <wmtk/simplex/Simplex.hpp>
 #include <wmtk/simplex/top_dimension_cofaces.hpp>
+#include <wmtk/utils/Logger.hpp>
 #include <wmtk/utils/primitive_range.hpp>
 
 namespace wmtk::invariants {
@@ -57,7 +58,10 @@ bool Invariant::directly_modified_after(
 
     return true;
 }
-
+bool Invariant::is_collection() const
+{
+    return false;
+}
 bool Invariant::use_old_state_in_after() const
 {
     return m_use_old_state_in_after;
diff --git a/src/wmtk/invariants/Invariant.hpp b/src/wmtk/invariants/Invariant.hpp
index 12bbdc9746..cabbbf9c31 100644
--- a/src/wmtk/invariants/Invariant.hpp
+++ b/src/wmtk/invariants/Invariant.hpp
@@ -1,4 +1,5 @@
 #pragma once
+#include <array>
 #include <vector>
 #include <wmtk/PrimitiveType.hpp>
 namespace wmtk {
@@ -30,6 +31,7 @@ class Invariant
 
     const Mesh& mesh() const;
 
+    // A compact pipeline for evaluating after without computing any cofaces
     // TODO change name
     virtual bool directly_modified_after(
         const std::vector<simplex::Simplex>& simplices_before,
@@ -41,12 +43,15 @@ class Invariant
     bool use_old_state_in_after() const;
     bool use_new_state_in_after() const;
 
+    virtual bool is_collection() const;
+
 private:
     const Mesh& m_mesh;
     const bool m_use_before = true;
     const bool m_use_old_state_in_after = true;
     const bool m_use_new_state_in_after = true;
 
+protected:
     const std::vector<Tuple> get_top_dimension_cofaces(
         const std::vector<simplex::Simplex>& simplices) const;
 };
diff --git a/src/wmtk/invariants/InvariantCollection.cpp b/src/wmtk/invariants/InvariantCollection.cpp
index cb1d804a8b..94d66c140c 100644
--- a/src/wmtk/invariants/InvariantCollection.cpp
+++ b/src/wmtk/invariants/InvariantCollection.cpp
@@ -2,12 +2,15 @@
 #include <type_traits>
 #include <wmtk/Mesh.hpp>
 #include <wmtk/simplex/Simplex.hpp>
+#include <wmtk/utils/Logger.hpp>
 
 namespace wmtk::invariants {
 
 InvariantCollection::InvariantCollection(const Mesh& m)
     : Invariant(m, true, true, true)
-{}
+{
+    m_use_same_mesh_caching = true;
+}
 InvariantCollection::~InvariantCollection() = default;
 InvariantCollection::InvariantCollection(const InvariantCollection&) = default;
 InvariantCollection::InvariantCollection(InvariantCollection&&) = default;
@@ -26,7 +29,10 @@ InvariantCollection& InvariantCollection::operator=(InvariantCollection&& o)
 
 void InvariantCollection::add(std::shared_ptr<Invariant> invariant)
 {
-    m_invariants.emplace_back(std::move(invariant));
+    const auto& invar = m_invariants.emplace_back(std::move(invariant));
+    if (m_use_same_mesh_caching && &mesh() == &invar->mesh()) {
+        m_same_mesh_invariants.emplace_back(invar);
+    }
 }
 bool InvariantCollection::before(const simplex::Simplex& t) const
 {
@@ -113,12 +119,62 @@ bool InvariantCollection::directly_modified_after(
                     mapped_simplices_after)) {
                 return false;
             }
-        } else {
+        } else if (!m_use_same_mesh_caching) {
             if (!invariant->directly_modified_after(simplices_before, simplices_after)) {
                 return false;
             }
         }
     }
+    if (m_use_same_mesh_caching) {
+        std::vector<Tuple> tuples_before, tuples_after;
+        return directly_modified_after_cached(
+            simplices_before,
+            simplices_after,
+            tuples_before,
+            tuples_after);
+    }
+    return true;
+}
+bool InvariantCollection::is_collection() const
+{
+    return true;
+}
+
+bool InvariantCollection::directly_modified_after_cached(
+    const std::vector<simplex::Simplex>& simplices_before,
+    const std::vector<simplex::Simplex>& simplices_after,
+    std::vector<Tuple>& cofaces_before,
+    std::vector<Tuple>& cofaces_after) const
+{
+    for (const auto& invariant_ptr : m_same_mesh_invariants) {
+        const auto& invariant = *invariant_ptr;
+        assert(&mesh() == &invariant.mesh());
+        if (invariant.is_collection()) {
+            if (!static_cast<const InvariantCollection&>(invariant).directly_modified_after_cached(
+                    simplices_before,
+                    simplices_after,
+                    cofaces_before,
+                    cofaces_after)) {
+                return false;
+            }
+        } else if (invariant.use_after()) {
+            if (invariant.use_new_state_in_after()) {
+                if (cofaces_after.empty()) {
+                    cofaces_after = get_top_dimension_cofaces(simplices_after);
+                }
+            }
+            if (invariant.use_old_state_in_after()) {
+                if (cofaces_before.empty()) {
+                    cofaces_before = mesh().parent_scope(
+                        [&]() { return get_top_dimension_cofaces(simplices_before); });
+                }
+            }
+
+            if (!after(cofaces_before, cofaces_after)) {
+                return false;
+            }
+        }
+    }
     return true;
 }
 
@@ -164,4 +220,5 @@ InvariantCollection::get_map_mesh_to_invariants()
     //
 }
 
+
 } // namespace wmtk::invariants
diff --git a/src/wmtk/invariants/InvariantCollection.hpp b/src/wmtk/invariants/InvariantCollection.hpp
index ab257c0428..a4fdbcd0fa 100644
--- a/src/wmtk/invariants/InvariantCollection.hpp
+++ b/src/wmtk/invariants/InvariantCollection.hpp
@@ -29,8 +29,17 @@ class InvariantCollection : public Invariant
 
     bool directly_modified_after(
         const std::vector<simplex::Simplex>& simplices_before,
-        const std::vector<simplex::Simplex>& simplices_after) const override;
+        const std::vector<simplex::Simplex>& simplices_after) const final override;
 
+    // optimization for evaluating connected subgraphs of invariants that share the same mesh
+    // In this case we can cache the cofaces computed once rather than re-evaluate them
+    bool directly_modified_after_cached(
+        const std::vector<simplex::Simplex>& simplices_before,
+        const std::vector<simplex::Simplex>& simplices_after,
+        std::vector<Tuple>& cofaces_before,
+        std::vector<Tuple>& cofaces_after) const;
+
+    bool is_collection() const final override;
     // pass by value so this can be internally moved
     void add(std::shared_ptr<Invariant> invariant);
 
@@ -44,6 +53,8 @@ class InvariantCollection : public Invariant
 
 private:
     std::vector<std::shared_ptr<Invariant>> m_invariants;
+    std::vector<std::shared_ptr<Invariant>> m_same_mesh_invariants;
+    bool m_use_same_mesh_caching = false;
 };
 
 } // namespace invariants
diff --git a/src/wmtk/multimesh/MultiMeshManager.cpp b/src/wmtk/multimesh/MultiMeshManager.cpp
index 5b824734a8..24a1e3543f 100644
--- a/src/wmtk/multimesh/MultiMeshManager.cpp
+++ b/src/wmtk/multimesh/MultiMeshManager.cpp
@@ -504,10 +504,14 @@ std::vector<Tuple> MultiMeshManager::map_tuples(
 
     int64_t depth = my_id.size();
 
-    auto [root_ref, tuple] = map_up_to_tuples(my_mesh, my_simplex, depth);
-    const simplex::Simplex simplex(root_ref, my_simplex.primitive_type(), tuple);
+    if (is_root()) {
+        return my_mesh.m_multi_mesh_manager.map_down_relative_tuples(my_mesh, my_simplex, other_id);
+    } else {
+        auto [root_ref, tuple] = map_up_to_tuples(my_mesh, my_simplex, depth);
+        const simplex::Simplex simplex(root_ref, my_simplex.primitive_type(), tuple);
 
-    return root_ref.m_multi_mesh_manager.map_down_relative_tuples(root_ref, simplex, other_id);
+        return root_ref.m_multi_mesh_manager.map_down_relative_tuples(root_ref, simplex, other_id);
+    }
 }
 
 std::vector<Tuple> MultiMeshManager::lub_map_tuples(
@@ -524,16 +528,23 @@ std::vector<Tuple> MultiMeshManager::lub_map_tuples(
 
     int64_t depth = my_id.size() - lub_id.size();
 
-    auto [local_root_ref, tuple] = map_up_to_tuples(my_mesh, my_simplex, depth);
-    assert(other_mesh.m_multi_mesh_manager.is_child(other_mesh, local_root_ref));
+    auto other_relative_id = relative_id(lub_id, other_id);
+    if (depth == 0) {
+        return my_mesh.m_multi_mesh_manager.map_down_relative_tuples(
+            my_mesh,
+            my_simplex,
+            other_relative_id);
+    } else {
+        auto [local_root_ref, tuple] = map_up_to_tuples(my_mesh, my_simplex, depth);
+        assert(other_mesh.m_multi_mesh_manager.is_child(other_mesh, local_root_ref));
 
-    const simplex::Simplex simplex(local_root_ref, my_simplex.primitive_type(), tuple);
+        const simplex::Simplex simplex(local_root_ref, my_simplex.primitive_type(), tuple);
 
-    auto other_relative_id = relative_id(lub_id, other_id);
-    return local_root_ref.m_multi_mesh_manager.map_down_relative_tuples(
-        local_root_ref,
-        simplex,
-        other_relative_id);
+        return local_root_ref.m_multi_mesh_manager.map_down_relative_tuples(
+            local_root_ref,
+            simplex,
+            other_relative_id);
+    }
 }
 
 simplex::Simplex MultiMeshManager::map_to_root(
diff --git a/src/wmtk/operations/attribute_update/AttributeTransferStrategyBase.cpp b/src/wmtk/operations/attribute_update/AttributeTransferStrategyBase.cpp
index de3629d6b8..c2f788ba0c 100644
--- a/src/wmtk/operations/attribute_update/AttributeTransferStrategyBase.cpp
+++ b/src/wmtk/operations/attribute_update/AttributeTransferStrategyBase.cpp
@@ -48,25 +48,25 @@ std::vector<Tuple> AttributeTransferStrategyBase::get_parent_simplices(
 
     if (my_primitive_type != parent_primitive_type) {
         // lambda for running either of the cases
-        std::vector<Tuple> r;
         if (parent_tuples.size() == 1) {
-            r = simplex::neighbors_single_dimension_tuples(
+            parent_tuples = simplex::neighbors_single_dimension_tuples(
                 m,
-                simplex::Simplex(m, my_primitive_type, parent_tuples[0]),
+                simplex::Simplex(my_primitive_type, parent_tuples[0]),
                 parent_primitive_type);
         } else {
+            std::vector<Tuple> r;
             for (const auto& parent_tup : parent_tuples) {
                 std::vector<Tuple> c = simplex::neighbors_single_dimension_tuples(
                     m,
-                    simplex::Simplex(m, my_primitive_type, parent_tup),
+                    simplex::Simplex(my_primitive_type, parent_tup),
                     parent_primitive_type);
                 std::copy(c.begin(), c.end(), std::back_inserter(r));
             }
             if (parent_tuples.size() > 1) {
                 simplex::utils::unique_homogeneous_simplices_inline(m, parent_primitive_type, r);
             }
+            parent_tuples = std::move(r);
         }
-        parent_tuples = std::move(r);
     }
     return parent_tuples;
 }
diff --git a/src/wmtk/simplex/Simplex.hpp b/src/wmtk/simplex/Simplex.hpp
index 75d1055cc4..16098cf41c 100644
--- a/src/wmtk/simplex/Simplex.hpp
+++ b/src/wmtk/simplex/Simplex.hpp
@@ -32,7 +32,6 @@ class Simplex
     Tuple m_tuple;
 
 public:
-    // the mesh class can use this index value to cache/accelerate operations
     Simplex(const PrimitiveType& ptype, const Tuple& t)
         : m_primitive_type{ptype}
         , m_tuple{t}