The NA62 experiment at CERN reports searches for K+→μ+N and K+→μ+νX decays, where N and X are massive invisible particles, using the 2016–2018 data set. The N particle is assumed to be a heavy neutral lepton, and the results are expressed as upper limits of O(10−8) of the neutrino mixing parameter |Uμ4|2 for N masses in the range 200–384 MeV/c2 and lifetime exceeding 50 ns. The X particle is considered a scalar or vector hidden sector mediator decaying to an invisible final state, and upper limits of the decay branching fraction for X masses in the range 10–370 MeV/c2 are reported for the first time, ranging from O(10−5) to O(10−7). An improved upper limit of 1.0×10−6 is established at 90% CL on the K+→μ+ννν¯ branching fraction.