  Three Mo-based transition metal dichalcogenides MoS$_2$, MoSe$_2$ and
MoTe$_2$ share at ambient conditions the same structure 2H$_c$, consisting of
layers where Mo atoms are surrounded by six chalcogen atoms in trigonal prism
coordination. The knowledge of their high-pressure behaviour is, however,
limited, particularly in case of MoSe$_2$ and MoTe$_2$. The latter materials do
not undergo a layer-sliding transition 2H$_c$ $\rightarrow$ 2H$_a$ known in
MoS$_2$ and currently no other stable phase besides 2H$_c$ is known in these
systems at room temperature. Employing evolutionary crystal structure
prediction in combination with \textit{ab initio} calculations we study the
zero-temperature phase diagram of both materials up to Mbar pressures. We find
a tetragonal phase with space group \textit{P4/mmm}, previously predicted in
MoS$_2$, to become stable in MoSe$_2$ at 118 GPa. In MoTe$_2$ we predict at 50
GPa a transition to a new layered tetragonal structure with space group
\textit{I4/mmm}, similar to CaC$_2$, where Mo atoms are surrounded by eight Te
atoms. The phase is metallic already at the transition pressure and becomes a
good metal beyond 1 Mbar. We discuss chemical trends in the family of Mo-based
transition metal dichalcogenides and suggest that MoTe$_2$ likely offers the
easiest route towards the post-2H phases.
