I'm guessing if Quantum Mechanics get modified to allow for physical collapse, the Schrodinger equation is modified. But whatever has already verified Quantum Mechanics thus far, the new theory needs to account for those results but, I would assume, make different predictions in other areas that haven't been tested, in comparison to QM. What would one example of where QM and the new theories would disagree (apart from the latter including collapse)? Is the experimental difference between the two inclined to be in the macroscopic scale? Or are there processes in the microscopic world that haven't been tested, where QM and new collapse theories would offer different predictions? EDIT: I dare say that if QM and the other theories give the same predictions where experimentally verification has been seen, then technically one could allow hidden variables to exist in the new theory. Even if there is no definite prediction for which state actualises in new theories, you could possibly allow one to have hidden variables choosing that result - as is the case in addition to standard QM.