We report the results of a study of multi-muon events produced at the Fermilab Tevatron collider and acquired with the CDF II detector using a dedicated dimuon trigger. The production cross section and kinematics of events in which both muon candidates are produced inside the beam pipe of radius 1.5 cm are successfully modeled by known processes which include heavy flavor production. In contrast, we are presently unable to fully account for the number and properties of the remaining events, in which at least one muon candidate is produced outside of the beam pipe, in terms of the same understanding of the CDF II detector, trigger, and event reconstruction.