The parameter space is usually (not only) a two dimensional plot of mass and the coupling force parameter. Those can give you a space that you would want to exp

The parameter space is usually (not only) a two dimensional plot of mass and the coupling force parameter. Those can give you a space that you would want to explore. There will be no one experiment that would give you sensitivity in all the parameter space. So you design experiments and collect data. If you don't find in the region your experiment were sensitive too (and you did your analysis carefully) then you establish a limit that says basically it cannot be in this region, look in other regions, then repeat. The analogy with your wallet is misleading because we know your habits, we don't know about nature habits. As I explained, when we exhaust the parameter space regions and can't find anything then this would tell us to give a shot to something else. Not that people are not doing this now already anyways.