Sure they can fit any experimental result that way, they can probably fit any 19 experimental results that way, but in general if you would freely adjust a constant to fit one experiment then it would stop fitting other experiments.
As a sibling comment points out, it is difficult to implement the markup that spans the space of all possible theories. Kostelecky's parametric Standard Model Extension offers one avenue to do so.
One could implement such a test as a checklist, too, which might already make a difference.