This article introduces a new class of searches for physics beyond the Standard Model that improves the sensitivity to signals with high jet multiplicity. The proposed searches gain access to high multiplicity signals by reclustering events into large-radius, or "fat," jets and by requiring that each event has multiple massive jets. This technique is applied to supersymmetric scenarios in which gluinos are pair-produced and then subsequently decay to final states with either moderate quantities of missing energy or final states without missing energy. In each of these scenarios, the use of jet mass improves the estimated reach in gluino mass by 20 % to 50 % over current LHC searches. Show Partial Abstract