Like the sibling comment says: we’re currently doing this. Higher energies are not really feasible without a bigger ring though so we’re increasing the beam in

Like the sibling comment says: we’re currently doing this. Higher energies are not really feasible without a bigger ring though so we’re increasing the beam intensity (sort of) to produce more physics per time unit. This very likely won’t reveal any new physics processes, but it will allow us to increase the precision in many measurements we do and could allow us to find discrepancies or otherwise increase our understanding of the existing model. This is effectively a measure to maximize the output we can get from the machine, so to maximize the return in investment. There’s a lot of debate in the field what should happen next. FCC is one possibility, but I’m personally sceptical (even though I work at CERN myself). It seems to me there’s a clear need for a Higgs-factory as a follow up to LHC, but that doesn’t have to be a ring collider, a electron positron linear collider could fulfill this purpose as well.