I'm curious: If you add a new axiom in order to make a undecidable proposition decidable, will this new axiom add more than one undecidable proposition, or is the number of new undecidable propositions unknown? Or are there infinitely undecidable propositions for every set of rules?

If the former is true, couldn't we theoretically just apply axioms in order to solve undecidable propositions which have a practical application if solved? Or will it practically be hard to find these axioms?