  Let H^2_m be the Drury-Arveson (DA) module which is the reproducing kernel
Hilbert space with the kernel function (z, w) \in B^m \times B^m \raro (1 -
<z,w>)^{-1}. We investigate for which multipliers \theta : \mathbb{B}^m \raro
\cll(\cle, \cle_*) the quotient module \clh_{\theta} is similar to H^2_m
\otimes \clf for some Hilbert space \clf, where M_{\theta} is the corresponding
multiplication operator in \cll(H^2_m \otimes \cle, H^2_m \otimes \cle_*) for
Hilbert spaces \cle and \cle_* and \clh_{\theta} is the quotient module (H^2_m
\otimes \cle_*)/ {clos} [M_{\theta}(H^2_m \otimes \cle)]. We show that a
necessary condition is the existence of a multiplier $\psi$ in \clm(\cle_*,
\cle) such that \theta \psi \theta = \theta. Moreover, we show that the
converse is equivalent to a structure theorem for complemented submodules of
H^2_m \otimes \cle for a Hilbert space \cle, which is valid for the case of
m=1. The latter result generalizes a known theorem on similarity to the
unilateral shift, but the above statement is new. Further, we show that a
finite resolution of DA-modules of arbitrary multiplicity using partially
isometric module maps must be trivial. Finally, we discuss the analogous
questions when the underlying operator tuple or algebra is not necessarily
commuting. In this case the converse to the similarity result is always valid.
