  We consider the critical behavior associated with incommensurate
unidirectional charge-density-wave ordering in a weakly orthorhombic system
subject to uniaxial strain as an experimentally significant example of
$U(1)\times U(1)$ multicriticality. We show that, depending on microscopic
details, the phase diagram can have qualitatively different structures which
can involve a vestigial meta-nematic critical point, a pair of tricritical
points, a decoupled tetracritical point, or (at least at mean-field level) a
bicritical point. We analyze the emergent symmetries in the critical regime and
find that these can -- at least in some cases -- involve an emergent
$\mathbb{Z}_2$ order parameter symmetry.
