  This paper focuses on the Private Linear Transformation (PLT) problem in the
multi-server scenario. In this problem, there are $N$ servers, each of which
stores an identical copy of a database consisting of $K$ independent messages,
and there is a user who wishes to compute $L$ independent linear combinations
of a subset of $D$ messages in the database while leaking no information to the
servers about the identity of the entire set of these $D$ messages required for
the computation. We focus on the setting in which the coefficient matrix of the
desired $L$ linear combinations generates a Maximum Distance Separable (MDS)
code. We characterize the capacity of the PLT problem, defined as the supremum
of all achievable download rates, for all parameters $N, K, D \geq 1$ and
$L=1$, i.e., when the user wishes to compute one linear combination of $D$
messages. Moreover, we establish an upper bound on the capacity of PLT problem
for all parameters $N, K, D, L \geq 1$, and leveraging some known capacity
results, we show the tightness of this bound in the following regimes: (i) the
case when there is a single server (i.e., $N=1$), (ii) the case when $L=1$, and
(iii) the case when $L=D$.
