Is it possible to count all possible Solutions of a Problem?

There may be something else you can do: You could use a preintsol callback to just reject any solution Xpress finds and also inject a no-good cut for that solution to avoid finding it again.

With this strategy you would have to collect the solutions yourself (because Xpress would never see a feasible solution) and you may not get all solutions to your problem.

But maybe the set of solutions you get is still good enough in this case?