  The recent proposal of non-Abelian boson-fermion dualities in 2+1 dimensions,
which morally relate $U(k)_N$ to $SU(N)_{-k}$ Chern-Simons-matter theories,
presents a new platform for exploring the landscape of non-Abelian quantum Hall
states accessible from theories of Abelian composite particles. Here we focus
on dualities relating theories of Abelian quantum Hall states of bosons or
fermions to theories of non-Abelian "composite fermions" partially filling
Landau levels. We show that these dualities predict special filling fractions
where both Abelian and non-Abelian composite fermion theories appear capable of
hosting distinct topologically ordered ground states, one Abelian and the other
a non-Abelian, $U(k)_2$ Blok-Wen state. Rather than being in conflict with the
duality, we argue that these results indicate unexpected dynamics in which the
infrared and lowest Landau level limits fail to commute across the duality. In
such a scenario, the non-Abelian topological order can be destabilized in favor
of the Abelian ground state, suggesting the presence of a phase transition
between the Abelian and non-Abelian states that is likely to be first order. We
also generalize these constructions to other non-Abelian fermion-fermion
dualities, in the process obtaining new derivations of a variety of paired
composite fermion phases using duality, including the anti-Pfaffian state.
Finally, we describe how, in multilayer constructions, excitonic pairing of the
composite fermions across $N$ layers can also generate the family of Blok-Wen
states with $U(k)_2$ topological order.
