  We study the fine structure in the spectrum of known and predicted
negative-parity hidden-charm exotic meson states, which comprise the lowest
$P$-wave multiplet in the dynamical diquark model. Starting with a form
previously shown to successfully describe the $S$-wave states, we develop a
5-parameter Hamiltonian that includes spin-orbit and tensor terms. After
discussing the experimental status of the observed $J^{PC} = 1^{--}$ states $Y$
with respect to masses and decay modes (classified by eigenvalues of
heavy-quark spin), we note a number of inconsistencies between measurements
from different experiments that complicate a unique determination of the
spectrum. Outlining a variety of scenarios for interpreting the $Y$ data, we
perform fits to each one, obtaining results that demonstrate differing
possibilities for the $P$-wave spectra. Choosing one of these fits for
illustration, we predict masses for all 28 isomultiplets in this $1P$
multiplet, compare the results to tantalizing hints in the data, and discuss
the rich discovery potential for new states.
