What about templates or namespaces?
Unfortunately, I am not sure such a compiler would be useful: even if
some user may want a small subset of C++ (look into the Embedded C++
"standard"), it might not be the same subset from one user to another.
And most importantly, the major C++ library API (for instance C++
input/output streams) are defined using a lot of C++ features
(including templates).
Look at the Qt toolkit for instance. Even if it claims to not use
several C++ features, in practice it needs a nearly fully compliant C++
compiler to be compiled, and still the Qt API itself is not using all C+
+ features (but it depends on the stdc++ library which uses more of
them)