Dark matter remains one of the greatest puzzles facing physics today. Our attempts to find a dark matter particle have so far come up empty-handed, and the theoretical models that have guided these efforts for the last 30 years are increasingly suspect. We still have few clues as to its nature. In this talk, I will make the case for broadening our view about the composition of dark matter by exploring models that predict the existence of more complex dark sectors. I will then describe in detail a novel and dedicated CMS Experiment search at the CERN LHC for one of these models, inelastic dark matter, which features two near-degenerate states in the dark sector (one of which is the stable dark matter) and a dark photon, the mediator of a new U(1) gauge symmetry in the dark sector similar to ordinary electromagnetism. The analysis exploits the long-lived nature of the decaying dark sector particle to reject backgrounds and attain sensitivity to inelastic dark matter and similar models with compressed spectra. This is the first dedicated collider search for inelastic dark matter, and as such can provide guidance and inspiration on how to effectively probe the open parameter space containing a rich dark sector phenomenology at the LHC.