Indirect searches at CMS

In these proceedings, we present several new measurements of Standard Model (SM) processes, in the Higgs sector and beyond, that push the precision frontier forward at CMS. Results are presented in the context of a framework parameterizing deviations in Higgs boson couplings, as well as in the context of SM Effective Field Theory, where new analyses targeting Higgs, top, and multi-boson processes probe an increasingly diverse set of operators. Within these frameworks, CMS is efficiently exploring a large space of new physics models. No significant deviation from SM expectations is found.