Yes a good question. If understand you, (probable but not certain) I guess I would say that " two theories, based on a different set of axioms/postulates, but with exactly the same verifiable results " ARE possible. I'm trying to think of some examples but I'm having difficulty...Here are some ideas and maybe you can give me better ones...
1. Copernican vs Ptolemaic astronomy
2. Neurology vs Freudian Psychology
3. Socio-biological ethics vs liberal Judeo-Christian morality
4. Western Medicine vs Eastern Medicine
5. Sociology vs Common Sense
Now, in all of these cases the first one has been said to have supplanted the second because the set of axioms is thought to be more rigorous and less wishy-washy. Yet they are often identical in terms of results (predictions/prescriptions/etc).
HOWEVER, these are all human constructs. I don’t see any problem with saying, “Reality is what it is, many theories can be made about one thing.” We discard the ones that sit wrong with our other ideas but that doesn’t make them invalid results-wise. Reality is unique, but the net to catch it in may vary. I mostly agree with
Wittgenstein’s Tractatus , insofar as I understand it.
Anyway, good question.