Neutrinos, the subatomic particles that play a fundamental role in everyday nuclear processes like the solar fusion cycle, are very much a mystery despite their discovery already 60 years ago. Within the Standard Model of Particle Physics, the widely successful description of particles at the smallest scales, neutrinos are massless. As a result, the Nobel Prize-winning discovery of extremely tiny neutrino masses represents one of the greatest cornerstones of modern physics. The ”Flavor, Lepton number, And Mass Explorations for Neutrinos at the COmpact muon solenoid” (FLAMENCO) project proposes a multi-national and multi-institutional effort to search for particles hypothesized by neutrino mass models. The search will be conducted with data collected by the Compact Muon Solenoid (CMS) detector at the CERN Large Hadron Collider (LHC), the world’s most energetic particle accelerator. The effort involves a coordinated collaboration between experimentalists and theorists to: (a) develop new software to model the production and decay of new particles at the LHC; (b) develop dedicated search strategies for unexplored scenarios that feature violation of lepton flavor and lepton number symmetries; and (c) carry out experimental searches on these precise windows to neutrino mass models with the CMS detector.