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Abstract New physics could manifest itself in the form of electroweak multiplets that interact at tree level with the Higgs boson but do not mix with Standard Model fields or acquire expectation values. In this paper, we study the potential contributions of such inert multiplets to several crucial Higgs properties, namely, the branching ratio of the Higgs to a Z boson and a photon (or massless dark photon) and the triple Higgs coupling. Constraints from the Higgs signal strengths, oblique parameters and unitarity are taken into account.