In this work, we investigate the prospects of future e+e- colliders in testing a Higgs triplet model with a scalar triplet and a scalar singlet under SU(2). The parameters of the model are fixed so that the lightest CP-even state corresponds to the Higgs particle observed at the LHC at around 125 GeV. This study investigates if the second heaviest CP-even, the heaviest CP-odd and the singly charged states can be observed at existing and future colliders by computing their accessible production and decay channels. In general, the LHC is not well equipped to produce a Higgs boson which is not mainly doubletlike, so we turn our focus to lepton colliders. We find distinctive features of this model in cases where the second heaviest CP-even Higgs is tripletlike, singletlike or a mixture. These features could distinguish the model from other scenarios at future e+e- colliders.