  We investigate binary mixtures undergoing phase separation after a second
(deeper) temperature quench into two- and three-phase coexistence regions. The
analysis is based on a lattice theory previously developed for gas-liquid
separation in generic mixtures. Our previous results, which considered an
arbitrary number of species and a single quench, showed that, due to slow
changes in composition, dense colloidal mixtures can phase-separate in two
stages. Moreover, the denser phase contains long-lived composition
heterogeneities that originate as the interfaces of shrunk domains. Here we
predict several new effects that arise after a second quench, mostly associated
with the extent to which crowding can slow down 'fractionation', i.e.
equilibration of compositions. They include long-lived regular arrangements of
secondary domains; wetting of fractionated interfaces by oppositely
fractionated layers; 'surface'-directed spinodal 'waves' propagating from
primary interfaces; a 'dead zone' where no phase separation occurs; and, in the
case of three-phase coexistence, filamentous morphologies arising out of
secondary domains.
