Abstract: The NA48/2 experiment at CERN collected a large sample of charged kaon decays to final states with multiple charged particles in 2003-2004. A new upper limit on the rate of the lepton number violating decay K-+/- -> pi(+/-)mu(+/-)mu(+/-) is reported: B( K-+/- -> pi(+/-)mu(+/-)mu(+/-)) < 8.6 x 10(-11) at 90% CL. Searches for two-body resonances X in K-+/- -> pi μμdecays (such as heavy neutral leptons N-4 and inflatons chi) are also presented. In the absence of signals, upper limits are set on the products of branching fractions B(K-+/- -> μN-+/-(4))B(N-4 -> pi mu) and B(K-+/- ->pi X-+/-)B(X -> mu(+),mu(-)) for ranges of assumed resonance masses and lifetimes. The limits are in the (10(-11),10(-9)) range for resonance lifetimes below 100 ps.