Abstract A generic search is presented for the associated production of a Z boson or a photon with an additional unspecified massive particle X, $${\textrm{pp}}\rightarrow {\textrm{pp}} +{{\textrm{Z}}}/\upgamma +{{\textrm{X}}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>pp</mml:mtext> <mml:mo>→</mml:mo> <mml:mtext>pp</mml:mtext> <mml:mo>+</mml:mo> <mml:mtext>Z</mml:mtext> <mml:mo>/</mml:mo> <mml:mi>γ</mml:mi> <mml:mo>+</mml:mo> <mml:mtext>X</mml:mtext> </mml:mrow> </mml:math> , in proton-tagged events from proton–proton collisions at $$\sqrt{s}=13\, \textrm{TeV}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> <mml:mo>=</mml:mo> <mml:mn>13</mml:mn> <mml:mspace/> <mml:mtext>TeV</mml:mtext> </mml:mrow> </mml:math> , 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 $${\textrm{pp}}\rightarrow {\textrm{pp}} +{{\textrm{Z}}}/\upgamma +{{\textrm{X}}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>pp</mml:mtext> <mml:mo>→</mml:mo> <mml:mtext>pp</mml:mtext> <mml:mo>+</mml:mo> <mml:mtext>Z</mml:mtext> <mml:mo>/</mml:mo> <mml:mi>γ</mml:mi> <mml:mo>+</mml:mo> <mml:mtext>X</mml:mtext> </mml:mrow> </mml:math> are set.