  We consider phase transitions and their contributions to vacuum energy in the
manifestly local theory of vacuum energy sequestering. We demonstrate that the
absence of instabilities imposes constraints on the couplings of gravitating
and non-gravitating sectors, which can be satisfied in a large class of models.
We further show by explicit construction that the vacuum energy contributions
to the effective cosmological constant in the descendant vacua are generically
strongly suppressed by the ratios of spacetime volumes of parent and descendant
geometries. This means that the cosmological constant in de Sitter descendant
vacua remains insensitive to phase transitions which may have occurred in the
course of its cosmic history.
