Once you have pre-specified some simplices $S$ that must be included in your triangulation
of the convex polytope $P$, what remains is the problem of triangulating a nonconvex region:
$P \setminus S$.
There are nonconvex polyhedra (in dimension 3) that cannot be triangulated.
I believe one could make such an example from the Schönhardt polyhedron,
by insisting on the inclusion of three tetrahedra ($S$) external to that polyhedron as
part of a triangulation of the convex hull ($P$) of two twisted triangles in parallel planes,
so that $P \setminus S$ is the un-tetrahedralizable Schönhardt polyhedron
(see below).
And it is an NP-complete problem to decide if a given nonconvex polyhedron can be triangulated,
a 1992 result of Ruppert and Seidel.

_{(Image from Wikipedia)}

If you want to nevertheless hope that your region can be triangulated, you might explore
geometric bistellar flips to underlie an approach.