  One of the simplest extensions of the Standard Model is the inclusion of an
additional scalar multiplet, and we consider scalars in the $SU(2)_L$ singlet,
triplet, and quartet representations. We examine models with heavy neutral
scalars, $m_H\sim 1-2$ TeV, and the matching of the UV complete theories to the
low energy effective field theory. We demonstrate the agreement of the
kinematic distributions obtained in the singlet models for the gluon fusion of
a Higgs pair with the predictions of the effective field theory. The
restrictions on the extended scalar sectors due to unitarity and precision
electroweak measurements are summarized and lead to highly restricted regions
of viable parameter space for the triplet and quartet models.
