  Two-dimensional rational CFT are characterised by an integer $\ell$, related
to the number of zeroes of the Wronskian of the characters. For two-character
RCFT's with $\ell<6$ there is a finite number of theories and most of these are
classified. Recently it has been shown that for $\ell \ge 6$ there are
infinitely many admissible characters that could potentially describe CFT's. In
this note we examine the $\ell=6$ case, whose central charges lie between 24
and 32, and propose a classification method based on cosets of meromorphic
CFT's. We illustrate the method using theories on Kervaire lattices with
complete root systems. In the process we construct the first known
two-character RCFT's beyond $\ell=2$.
