  We develop a proposal to realise a widely tunable and clean quantum phase
transition in bilayer graphene between two paradigmatic fractionalized phases
of matter: the Moore-Read fractional quantum Hall state and the composite Fermi
liquid metal. This transition can be realized at total fillings $\nu=\pm 3+1/2$
and the critical point can be controllably accessed by tuning either the
interlayer electric bias or the perpendicular magnetic field values over a wide
range of parameters. We study the transition numerically within a model that
contains all leading single particle corrections to the band-structure of
bilayer graphene and includes the fluctuations between the $n=0$ and $n=1$
cyclotron orbitals of its zeroth Landau level to delineate the most favorable
region of parameters to experimentally access this unconventional critical
point. We also find evidence for a new anisotropic gapless phase stabilized
near the level crossing of $n=0/1$ orbits.
