The Electron-Ion Collider will be a critical step forward for the collider community toward high-intensity, next generation polarized lepton-hadron collider physics. Member of the HEP community have been investigating the idea of an upgrade to the EIC, replacing the electron ring with a muon storage ring and creating a Muon-Ion Collider (MuIC). A MuIC in the same footprint at the EIC would be capable of center-of-mass energies that enable a wide program of study, including Higgs physics. I explore the possibility of specifically producing the Higgs and detecting its decay to charm quarks, an observation that would enable a further mapping of the Standard Model and the Higgs couplings to second-generation matter. I will outline some key challenges crossing theoretical and experimental issues and close with opportunities for advancing a potential Higgs program at a MuIC