In a purely multi-variable setting (i.e., the issues discussed in this note
are not interesting in the single variable operator theory setting), we show
that the coincidence of two operator valued Schur class multipliers of a
certain kind on the Drury-Arveson space is characterized by the fact that the
associated colligations (or a variant, obtained canonically) are `unitarily
coincident' in a sense to be made precise in the last section of this article
