A generic search is presented for the associated production of a Z boson or a photon with an additional unspecified massive particle X, $${\textrm{pp}}\rightarrow {\textrm{pp}} +{{\textrm{Z}}}/\upgamma +{{\textrm{X}}} $$, in proton-tagged events from proton–proton collisions at $$\sqrt{s}=13, \textrm{TeV}$$, recorded in 2017 with the CMS detector and the CMS-TOTEM precision proton spectrometer. The missing mass spectrum is analysed in the 600–1600 GeV range and a fit is performed to search for possible deviations from the background expectation. No significant excess in data with respect to the background predictions has been observed. Model-independent upper limits on the visible production cross section of $${\textrm{pp}}\rightarrow {\textrm{pp}} +{{\textrm{Z}}}/\upgamma +{{\textrm{X}}} $$are set.