  We prove a factorization theorem for reproducing kernel Hilbert spaces whose
kernel has a normalized complete Nevanlinna-Pick factor. This result relates
the functions in the original space to pointwise multipliers determined by the
Nevanlinna-Pick kernel and has a number of interesting applications. For
example, for a large class of spaces including Dirichlet and Drury-Arveson
spaces, we construct for every function $f$ in the space a pluriharmonic
majorant of $|f|^2$ with the property that whenever the majorant is bounded,
the corresponding function $f$ is a pointwise multiplier.
