  We derive functional convergence of the partial maxima stochastic processes
of multivariate linear processes with weakly dependent heavy-tailed innovations
and random coefficients. The convergence takes place in the space of
$\mathbb{R}^{d}$--valued c\`{a}dl\`{a}g functions on $[0,1]$ endowed with the
weak Skorokhod $M_{1}$ topology. We also show that this topology in general can
not be replaced by the standard (or strong) $M_{1}$ topology.
