  We show that for every connected analytic subvariety $V$ there is a
pseudoconvex set $\Omega$ such that every bounded matrix-valued holomorphic
function on $V$ extends isometrically to $\Omega$. We prove that if $V$ is two
analytic disks intersecting at one point, if every bounded scalar valued
holomorphic function extends isometrically to $\Omega$, then so does every
matrix-valued function. In the special case that $\Omega$ is the symmetrized
bidisk, we show that this cannot be done by finding a linear isometric
extension from the functions that vanish at one point.
