  Quantum spin liquids (QSL) have generated considerable excitement as phases
of matter with emergent gauge structures and fractionalized excitations. In
this context, phase transitions out of QSLs have been widely discussed as Higgs
transitions from deconfined to confined phases of a lattice gauge theory.
However the possibility of a wider range of novel phases, occuring between
these two limits, has yet to be systematically explored. In this Letter, we
develop a formalism which allows for interactions between fractionalised
quasiparticles coming from the constraint on the physical Hilbert space, and
can be used to search for exotic, hidden phases. Taking pyrochlore spin ice as
a starting point, we show how a U(1) QSL can give birth to abundant daughter
phases, without need for fine--tuning of parameters. These include a
(charged--) $\mathbb{Z}_2$ QSL, and a supersolid. We discuss implications for
experiment, and numerical results which support our analysis. These results are
of broad relevance to QSL subject to a parton description, and offer a new
perspective for searching exotic hidden phases in quantum magnets.
