Hooking into the built-in completion

Hi,
is there any way to hook into the built-in completion methods? In particular,
can I somehow capture the results and thereby combine it with other completion
functions by writing my own?
That would make things so much easier for so many use cases. In particular
combining completion functions with the built-in functionality and reversing
the order of <C-P> and such.
Is that already possible or, if not, is there a chance of adding such hooks?

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