  In this paper we solve $m$-parameter eigenvalue problems ($m$EPs), with $m$
any natural number by representing the problem using Tensor-Trains (TT) and
designing a method based on this format. $m$EPs typically arise when separation
of variables is applied to separable boundary value problems. Often, methods
for solving $m$EP are restricted to $m = 3$, due to the fact that, to the best
of our knowledge, no available solvers exist for $m>3$ and reasonable size of
the involved matrices. In this paper, we prove that computing the eigenvalues
of a $m$EP can be recast into computing the eigenvalues of TT-operators. We
adapted the algorithm in \cite{Dolgov2014a} for symmetric eigenvalue problems
in TT-format to an algorithm for solving generic $m$EPs. This leads to a
subspace method whose subspace dimension does not depend on $m$, in contrast to
other subspace methods for $m$EPS. This allows us to tackle $m$EPs with $m > 3$
and reasonable size of the matrices. We provide theoretical results and report
numerical experiments. The MATLAB code is publicly available.
