  The Read-Rezayi wave function is one of the candidates for the fractional
quantum Hall effect at filling fraction $\nu=2+\nicefrac{3}{5}$, and thereby
also its hole conjugate at $2+\nicefrac{2}{5}$. We study a general class of
"tripartite" composite fermion wave functions, which reduce to the Read-Rezayi
ground state and quasiholes for appropriate quantum numbers, but also allow a
construction of wave functions for quasiparticles and neutral excitations by
analogy to the standard composite fermion theory. We present numerical evidence
in finite systems that these trial wave functions capture well the low energy
physics of a 4-body model interaction. We also compare the tripartite composite
fermion wave functions with the exact Coulomb eigenstates at
$2+\nicefrac{3}{5}$, and find reasonably good agreement. The ground state as
well as several excited states of the 4-body interaction are seen to evolve
adiabatically into the corresponding Coulomb states for N=15 particles. These
results support the plausibility of the Read-Rezayi proposal for the
$2+\nicefrac{2}{5}$ and $2+\nicefrac{3}{5}$ fractional quantum Hall effect.
However, certain other proposals also remain viable, and further study of
excitations and edge states will be necessary for a decisive establishment of
the physical mechanism of these fractional quantum Hall states.
