  We propose a different route to time-reversal invariant Weyl semimetals
employing multilayer heterostructures comprising ordinary "trivial" insulators
and nontrivial insulators with \textit{pairs} of protected Dirac cones on the
surface. We consider both the case of weak topological insualtors, where
surface Dirac cones are pinned to time-reversal invariant momenta, and of
topological crystalline insulators with unpinned surface Dirac cones. For both
realizations we explain phenomenologically how the proposed construction leads
to the emergence of a Weyl semimetal phase. We further formulate effective
low-energy models for which we prove the existence of semimetallic phases with
four isolated Weyl points. Finally, we discuss how the proposed design can be
realized experimentally with state-of-the-art technologies.
