  This work considers an extension of the Standard Model (SM) Higgs sector by a
real, scalar singlet field, including applicability to a dark matter (DM) model
with the addition of a Yukawa coupling to a Dirac fermion. The collider
signatures and constraints on the mixed two-Higgs scenario are determined,
including limits from Higgs production signals and exclusion searches, as well
as constraints arising from the Higgs total and invisible widths. As there is
overwhelming Higgs data which is consistent with a SM scenario, the case in
which an additional scalar has evaded detection is further explored in the
context of Higgs precision measurement. The discovery reach and prospective
signatures of the model at a proposed linear collider are investigated, with
particular focus on the Higgs triple coupling, and di-Higgs production
processes.
