  The fractional quantum Hall (FQH) states are exotic quantum many-body phases
whose elementary charged excitations are neither bosons nor fermions but
anyons, obeying fractional braiding statistics. While most FQH states are
believed to have Abelian anyons, the Moore-Read type states with even
denominators, appearing at half filling of a Landau level (LL), are predicted
to possess non-Abelian excitations with appealing potentials in topological
quantum computation. These states, however, depend sensitively on the orbital
contents of the single-particle LL wavefunction and the mixing between
different LLs. Although they have been observed in a few materials, their
non-Abelian statistics still awaits experimental confirmation. Here we show
magnetotransport measurements on Bernal-stacked trilayer graphene (TLG), whose
unique multiband structure facilitates the interlaced LL mixing, which can be
controlled by external magnetic and displacement fields. We observe a series of
robust FQH states including even-denominator ones at filling factors
$\nu=-9/2$, $-3/2$, $3/2$ and $9/2$. In addition, we are able to finetune the
LL mixing and crossings to drive quantum phase transitions of these
half-filling states and their neighboring odd-denominator ones, exhibiting a
related emerging and waning behavior. Our results establish TLG as a
controllable system for tuning the weights of LL orbitals and mixing strength,
and a fresh platform to seek for non-Abelian quasi-particles.
