There is no "Higgs experiment". The LHC collides protons with protons, and those collisions produce all sorts of particles as long as they are not too heavy. The production of a Higgs boson is just one of many processes which can happen in an interaction. If there are other new particles, they could be produced as well, and the LHC detectors look for those particles, too.
At electron-positron-colliders (like LEP, or the planned ILC), this is different - usually you have to choose which process you want to study, and adjust the energy accordingly.