  Modular invariant conformal field theories with just one primary field and
central charge $c=24$ are considered. It has been shown previously that if the
chiral algebra of such a theory contains spin-1 currents, it is either the
Leech lattice CFT, or it contains a Kac-Moody sub-algebra with total central
charge 24. In this paper all meromorphic modular invariant combinations of the
allowed Kac-Moody combinations are obtained. The result suggests the existence
of 71 meromorphic $c=24$ theories, including the 41 that were already known.
