  A new class of bootstrap percolation models in which particle culling occurs
only for certain numbers of nearest neighbours is introduced and studied on a
Bethe lattice. Upon increasing the density of initial configuration they
undergo multiple hybrid (or mixed-order) phase transitions, showing that such
intriguing phase behaviours may also appear in fully homogeneous
situations/environments, provided that culling is selective rather than
cumulative. The idea immediately extends to facilitation dynamics, suggesting a
simple way to construct one-component models of multiple glasses and
glass-glass transitions as well as more general coarse-grained models of
complex cooperative dynamics.
