  Recent work has demonstrated that Clark's theory of unitary perturbations of
the backward shift restricted to a deBranges-Rovnyak subspace of Hardy space on
the disk has a natural extension to the several variable setting. In the
several variable case, the appropriate generalization of the Schur class of
contractive analytic functions is the closed unit ball of the Drury-Arveson
multiplier algebra and the Aleksandrov-Clark measures are necessarily promoted
to positive linear functionals on a symmetrized subsystem of the Cuntz-Toeplitz
operator system A + A*, where A is the non-commutative disk algebra. We
continue this program for vector-valued Drury-Arveson space by establishing the
existence of a canonical `tight' extension of any Aleksandrov-Clark map to the
full Cuntz-Toeplitz operator system. We apply this tight extension to
generalize several earlier results and we characterize all extensions of the
Aleksandrov-Clark maps.
