If a theory adds primal axioms to a formerly confirmed theory, but does not provide novel predictions (or those predictions are not testable), then the competition of the two competing theories is, in my mind, undecidable from a scientific point of view - unless the latter more primal theory can directly derive the former less primal theory. That is, as long as both theories are adequate from a theoretical perspective (e.g., overall logico-mathematically consistent, etc), then two competing theories are undecidable if there are no novel predictions that favor one and dispute the other. Giving primacy to the latter theory simply because it is deducible from 'undoubtable' axioms is not good enough from a science perspective, in my opinion. I know of changes that could be made to discarded theories having 'good' axioms (i.e., axioms having undoubted reliablity to the timeperiod they were considered undeniable), and if those theoretical changes were made at the time (to save this old theory), then the discarded theory would never have been supplanted by the new theory
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In my mind there never will be a TOE. There may be a more fundamental theory like Loop Quantum Gravity with more fundamental axioms that can derive relativity and quantum theory and even spacetime, and perhaps even string theory. But it is very unlikely to be uniquely testable. It will be most useful at scales that we cannot observe, which essentially makes it metaphysics.

In analogy, the TOE will be a very small part of the whole body of science. At best it will be able to derive some of the constants of the Standard Theory, which will make it a grand success. But I doubt that that will happen. Science will still rest on the foot of physics, supported by the leg of chemistry, with all the real action in the body of biology.