This is why I think that modeling elementary physics is nothing else than fitting data. We might end up with something that we perceive as "simple", or not. But in any case all the fitting has been hidden in the process of ruling out models. It's just that a lot of the fitting process is (implicitly) being done by theorists; we come up with new models and that are then being falsified.

For example, how many parameters does the Standard Model have? It's not clear what you count as a parameter. Do you count the group structure, the other mathematical structure that has been "fitted" through decades of comparisons with experiments?

It tends to be a parameter that can be derived from rrasoning and assumptions. This contrasts to free parameters where you say "and we have no idea what this value should be, so we'll measure it"

Yes, it is.

Which makes the only truly zero parameter system the collection of all systems, in all forms.

Kolmogorov complexity[0] solves this loophole :)

[0] https://en.wikipedia.org/wiki/Kolmogorov_complexity