How to Build a Geometric Theory?

What's the best way to create a geometric theory? Is it to start with axioms and use logical deduction to see what follows? Is it to start with a theory that works and try to work backward to discover the fundamentals?

What happens when we discover little problems within a dominant, useful theory? Do we add little epicycles to the theory, or do we start over from scratch?

My approach is to start from the phenomena we experience (the fundamentals), then posit base-level objects and axioms. From this foundation, we then derive and discover more advanced theories.

And if we discover problems with a dominant theory - logical or empirical problems - then we need to re-examine the foundations and be willing to start over from scratch.

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