  The nature of the many-body localization (MBL) transition and even the
existence of the MBL phase in random many-body quantum systems have been
actively debated in recent years. In spatial dimension $d>1$, there is some
consensus that the MBL phase is unstable to rare thermal inclusions that can
lead to an avalanche that thermalizes the whole system. In this note, we
explore the possibility of MBL in quasiperiodic systems in dimension $d>1$. We
argue that (i) the MBL phase is stable at strong enough quasiperiodic
modulations for $d = 2$, and (ii) the possibility of an avalanche strongly
constrains the finite-size scaling behavior of the MBL transition. We present a
suggestive construction that MBL is unstable for $d \geq 3$.
