There are plenty of extensions of the Standard Model, that all agree until the energy scales that have already been explored, but will differ at the new energy range of 14 TeV. This means the data should be able to distinguish between the predictions of these different theories.
But it seems that, thanks to all the unknown parameters that go into each theory, if the data show features that are at odds with the predictions, it's possible that fine-tuning the parameters will get the theory in agreement with data again.
I understand this has happened to fit the data of the previous run.
My question is this then. Are there possible observations that would rule out a whole family of theories in a definitive manner?