  We present the general form of the renormalizable four-point interactions of
a complex scalar field furnishing an irreducible representation of SU(2), and
derive a set of algebraic identities that facilitates the calculation of
higher-order radiative corrections. As an application, we calculate the
two-loop beta function for the SM extended by a scalar multiplet, and provide
the result explicitly in terms of the group invariants. Our results include the
evolution of the Higgs-portal couplings, as well as scalar "minimal dark
matter". We present numerical results for the two-loop evolution of the various
couplings.
