diff --git a/gap/libsemigroups/froidure-pin.gi b/gap/libsemigroups/froidure-pin.gi
index 163b78b2b..e4de024b0 100644
--- a/gap/libsemigroups/froidure-pin.gi
+++ b/gap/libsemigroups/froidure-pin.gi
@@ -48,16 +48,33 @@ Q -> CanUseLibsemigroupsCongruence(QuotientSemigroupCongruence(Q)));
 ###########################################################################
 
 DeclareOperation("FroidurePinMemFnRec", [IsSemigroup]);
+DeclareOperation("FroidurePinMemFnRec",
+                 [IsSemigroup, IsListOrCollection]);
 
-InstallMethod(FroidurePinMemFnRec, "for a transformation semigroup",
-[IsTransformationSemigroup],
-function(S)
-  if DegreeOfTransformationSemigroup(S) <= 16
+InstallMethod(FroidurePinMemFnRec, "for a semigroup",
+[IsSemigroup], S -> FroidurePinMemFnRec(S, []));
+
+InstallMethod(FroidurePinMemFnRec, "for a semigroup",
+[IsSemigroup, IsListOrCollection], {S, coll} -> FroidurePinMemFnRec(S));
+
+InstallMethod(FroidurePinMemFnRec,
+"for a transformation semigroup and list or coll.",
+[IsTransformationSemigroup, IsListOrCollection],
+function(S, coll)
+  local N;
+  N := DegreeOfTransformationSemigroup(S);
+  if IsTransformationCollection(coll) then
+    N := Maximum(N, DegreeOfTransformationCollection(coll));
+  elif not IsEmpty(coll) then
+    Error("Expected a transf. coll. or empty list, found ",
+          TNAM_OBJ(coll));
+  fi;
+  if N <= 16
       and IsBound(LIBSEMIGROUPS_HPCOMBI_ENABLED) then
     return libsemigroups.FroidurePinTransf16;
-  elif DegreeOfTransformationSemigroup(S) <= 2 ^ 16 then
+  elif N <= 2 ^ 16 then
     return libsemigroups.FroidurePinTransfUInt2;
-  elif DegreeOfTransformationSemigroup(S) <= 2 ^ 32 then
+  elif N <= 2 ^ 32 then
     return libsemigroups.FroidurePinTransfUInt4;
   else
     # Cannot currently test the next line
@@ -65,12 +82,21 @@ function(S)
   fi;
 end);
 
-InstallMethod(FroidurePinMemFnRec, "for a partial perm semigroup",
-[IsPartialPermSemigroup],
-function(S)
+InstallMethod(FroidurePinMemFnRec,
+"for a partial perm. semigroup and list or coll.",
+[IsPartialPermSemigroup, IsListOrCollection],
+function(S, coll)
   local N;
   N := Maximum(DegreeOfPartialPermSemigroup(S),
                CodegreeOfPartialPermSemigroup(S));
+  if IsPartialPermCollection(coll) then
+    N := Maximum(N,
+                 DegreeOfPartialPermCollection(coll),
+                 CodegreeOfPartialPermCollection(coll));
+  elif not IsEmpty(coll) then
+    Error("Expected a partial perm. coll. or empty list, found ",
+          TNAM_OBJ(coll));
+  fi;
   if N <= 16 and IsBound(LIBSEMIGROUPS_HPCOMBI_ENABLED) then
     return libsemigroups.FroidurePinPPerm16;
   elif N <= 2 ^ 16 then
@@ -860,7 +886,7 @@ function(Constructor, S, coll, opts)
     Sort(coll, IsGreensDGreaterThanFunc(Semigroup(coll)));
   fi;
 
-  R := FroidurePinMemFnRec(S);
+  R := FroidurePinMemFnRec(S, coll);
 
   # Perform the closure
   if IsPartialPermSemigroup(S) or IsTransformationSemigroup(S) then
@@ -875,8 +901,6 @@ function(Constructor, S, coll, opts)
     fi;
     if M > N then
       # Can't use closure, TODO(later) use copy_closure
-      # FIXME(later) if M goes larger than the type of R can support this will
-      # end badly
       CppT  := R.make();
       add_generator := R.add_generator;
       for x in GeneratorsOfSemigroup(S) do
diff --git a/gapbind14/include/gapbind14/cpp_fn.hpp b/gapbind14/include/gapbind14/cpp_fn.hpp
index 371106a94..af973883f 100644
--- a/gapbind14/include/gapbind14/cpp_fn.hpp
+++ b/gapbind14/include/gapbind14/cpp_fn.hpp
@@ -35,7 +35,7 @@
 
 namespace gapbind14 {
 
-  constexpr size_t MAX_FUNCTIONS = 64;
+  constexpr size_t MAX_FUNCTIONS = 96;
   extern UInt      T_GAPBIND14_OBJ;
 
   ////////////////////////////////////////////////////////////////////////
diff --git a/src/to_cpp.hpp b/src/to_cpp.hpp
index 0bc9461c9..0ca1d3e45 100644
--- a/src/to_cpp.hpp
+++ b/src/to_cpp.hpp
@@ -27,8 +27,6 @@
 #include <algorithm>      // for max, min, sort
 #include <cstddef>        // for size_t
 #include <cstdint>        // for uint32_t
-#include <exception>      // for exception
-#include <functional>     // for __unwrap_reference<>::type
 #include <memory>         // for make_unique, unique_ptr
 #include <string>         // for string
 #include <type_traits>    // for decay_t, is_same, conditional_t
@@ -444,12 +442,26 @@ namespace gapbind14 {
         x[i] = i;
       }
     }
+    template <typename TransfType>
+    TransfType new_transf(size_t N) {
+      return TransfType(N);
+    }
+
+    template <>
+    inline HPCombi::Transf16 new_transf(size_t N) {
+      if (N > 16) {
+        ErrorQuit("expected transformation of degree at most 16, found %d",
+                  (Int) N,
+                  0L);
+      }
+      return HPCombi::Transf16();
+    }
 
   }  // namespace detail
 
-  template <typename Scalar>
-  struct to_cpp<Transf<0, Scalar>> {
-    using cpp_type = Transf<0, Scalar>;
+  template <typename TransfType>
+  struct ToTransf {
+    using cpp_type = TransfType;
 
     cpp_type operator()(Obj t) const {
       if (!IS_PLIST(t)) {
@@ -477,7 +489,7 @@ namespace gapbind14 {
                   (Int) DEG_TRANS(x));
       }
 
-      cpp_type result(N);
+      cpp_type result = detail::new_transf<cpp_type>(N);
       if (TNUM_OBJ(x) == T_TRANS2) {
         detail::to_cpp_transf(
             result, ADDR_TRANS2(x), std::min(DEG_TRANS(x), N));
@@ -492,6 +504,20 @@ namespace gapbind14 {
     }
   };
 
+  template <typename Scalar>
+  struct to_cpp<Transf<0, Scalar>> : ToTransf<Transf<0, Scalar>> {};
+
+#ifdef LIBSEMIGROUPS_HPCOMBI_ENABLED
+  template <>
+  struct to_cpp<HPCombi::Transf16> : public ToTransf<HPCombi::Transf16> {};
+
+  template <>
+  struct to_cpp<HPCombi::Transf16&> : ToTransf<HPCombi::Transf16> {};
+
+  template <>
+  struct to_cpp<HPCombi::Transf16 const&> : ToTransf<HPCombi::Transf16> {};
+#endif
+
   ////////////////////////////////////////////////////////////////////////
   // Partial perms
   ////////////////////////////////////////////////////////////////////////
@@ -532,11 +558,27 @@ namespace gapbind14 {
         x[i] = undef;
       }
     }
+
+    template <typename PPermType>
+    PPermType new_pperm(size_t N) {
+      return PPermType(N);
+    }
+
+    template <>
+    inline HPCombi::PPerm16 new_pperm(size_t N) {
+      if (N > 16) {
+        ErrorQuit("expected partial perm of degree at most 16, found %d",
+                  (Int) N,
+                  0L);
+      }
+      return HPCombi::PPerm16();
+    }
+
   }  // namespace detail
 
-  template <typename Scalar>
-  struct to_cpp<PPerm<0, Scalar>> {
-    using cpp_type = PPerm<0, Scalar>;
+  template <typename PPermType>
+  struct ToPPerm {
+    using cpp_type = PPermType;
 
     cpp_type operator()(Obj t) const {
       if (!IS_PLIST(t)) {
@@ -573,7 +615,8 @@ namespace gapbind14 {
             (Int) M);
       }
 
-      cpp_type result(N);
+      cpp_type result = detail::new_pperm<cpp_type>(N);
+
       if (TNUM_OBJ(x) == T_PPERM2) {
         detail::to_cpp_pperm(result, ADDR_PPERM2(x), DEG_PPERM2(x));
       } else if (TNUM_OBJ(x) == T_PPERM4) {
@@ -598,6 +641,20 @@ namespace gapbind14 {
     }
   };
 
+  template <typename Scalar>
+  struct to_cpp<PPerm<0, Scalar>> : ToPPerm<PPerm<0, Scalar>> {};
+
+#ifdef LIBSEMIGROUPS_HPCOMBI_ENABLED
+  template <>
+  struct to_cpp<HPCombi::PPerm16> : ToPPerm<HPCombi::PPerm16> {};
+
+  template <>
+  struct to_cpp<HPCombi::PPerm16&> : ToPPerm<HPCombi::PPerm16> {};
+
+  template <>
+  struct to_cpp<HPCombi::PPerm16 const&> : ToPPerm<HPCombi::PPerm16> {};
+#endif
+
   ////////////////////////////////////////////////////////////////////////
   // Bipartition
   ////////////////////////////////////////////////////////////////////////