  We investigate the Poincar\'e approach to computing 3d gravity partition
functions dual to Rational CFT. For a single genus-1 boundary, we show that for
certain infinite sets of levels, the SU(2)$_k$ WZW models provide unitary
examples for which the Poincare series is a positive linear combination of two
modular-invariant partition functions. This supports the interpretation that
the bulk gravity theory (a topological Chern-Simons theory in this case) is
dual to an average of distinct CFT's sharing the same Kac-Moody algebra. We
compute the weights of this average for all seed primaries and all relevant
values of k. We then study other WZW models, notably SU($N$)$_1$ and SU(3)$_k$,
and find that each class presents rather different features. Finally we
consider multiple genus-1 boundaries, where we find a class of seed functions
for the Poincar\'e sum that reproduces both disconnected and connected
contributions -- the latter corresponding to analogues of 3-manifold
"wormholes" -- such that the expected average is correctly reproduced.
