The full set of data collected by the CMS experiment at a center of mass energy of 13 TeV allows searches for rare production modes of the Higgs boson, subdominant with respect to the ones already observed at the LHC, by using a variety of decay modes profiting from the ones with largest expected branching fractions. They include associate production of the Higgs boson with two b-quarks, with a c-quark, or vector boson scattering production with two associated W bosons. Double Higgs boson production associated with a pair of top quarks is also considered. While the expected rate is still limited by the collected data, these modes become enhanced in several beyond standard model theories and can be used to constrain such models.