Well, GraalPython is a Python JIT compiler which can exploit dynamically determined types, and it advertises 4.3x faster, so it's possible to do drastically better than a few percent. I think that's state of the art but might be wrong.
Note that this is with a relatively small investment as these things go, the GraalPython team is about ~3 people I guess, looking at the GH repo. It's an independent implementation so most of the work went into being compatible with Python including native extensions (the hard part).
But this speedup depends a lot on what you're doing. Some types of code can go much faster. Others will be slower even than CPython, for example if you want to sandbox the native code extensions.
Pypy is a different JIT that gives anything from slower/same to 100x speedup depending on the benchmark. They give a geometric mean of 4.8x speedup across their suite of benchmarks.
https://speed.pypy.org/
