Three searches are presented for signatures of physics beyond the standard model (SM) in tau tau final states in proton-proton collisions at the LHC, using a data sample collected with the CMS detector at √<i>s</i> = 13 TeV, corresponding to an integrated luminosity of 138 fb^(-1). Upper limits at 95% confidence level (CL) are set on the products of the branching fraction for the decay into tau leptons and the cross sections for the production of a new boson phi, in addition to the H(125) boson, via gluon fusion (ggϕ) or in association with b quarks, ranging from O(10 pb) for a mass of 60 GeV to 0.3 fb for a mass of 3.5TeV each. The data reveal two excesses for ggϕ production with local p-values equivalent to about three standard deviations at m_ϕ = 0.1 and 1.2TeV. In a search for t-channel exchange of a vector leptoquark U-1, 95% CL upper limits are set on the dimensionless U1 leptoquark coupling to quarks and tau leptons ranging from 1 for a mass of 1TeV to 6 for a mass of 5TeV, depending on the scenario. In the interpretations of the M-h(125) and M-h,EFT(125) minimal supersymmetric SM benchmark scenarios, additional Higgs bosons with masses below 350 GeV are excluded at 95% CL.