  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 doublet-like, so we turn our focus to lepton colliders. We find
distinctive features of this model in cases when the second heaviest $CP-$even
Higgs is triplet-like, singlet-like or a mixture. These features could
distinguish the model from other scenarios at future $e^{+}e^{-}$ colliders.
