  Given a collection of test functions, one defines the associated Schur-Agler
class as the intersection of the contractive multipliers over the collection of
all positive kernels for which each test function is a contractive multiplier.
We indicate extensions of this framework to the case where the test functions,
kernel functions, and Schur-Agler-class functions are allowed to be matrix- or
operator-valued. We illustrate the general theory with two examples: (1) the
matrix-valued Schur class over a finitely-connected planar domain and (2) the
matrix-valued version of the constrained Hardy algebra (bounded analytic
functions on the unit disk with derivative at the origin constrained to have
zero value). Emphasis is on examples where the matrix-valued version is not
obtained as a simple higher-multiplicity tensoring of the scalar-valued
version.
