  In this work we extend the study of arXiv:2210.07186 by investigating two-
and three-character MLDEs for Fricke groups at prime levels. We have
constructed these higher-character MLDEs by using a $\mathit{novel}$
Serre-Ramanujan type derivative operator which maps $k$-forms to $(k+2)$-forms
in $\Gamma^{+}_0(p)$. We found that this $\mathit{novel}$ derivative
construction enabled us to write down a general prescription for obtaining
$\mathit{Ramanujan-Eisenstein}$ identities for these groups. We discovered
several $\mathit{novel}$ single-, two-, and three-character admissible
solutions for Fricke groups at levels $2$ and $3$ after solving the MLDEs among
which we have realized some in terms of Mckay-Thompson series and others in
terms of modular forms of the corresponding Hecke groups. Among these
solutions, we have identified interesting non-trivial bilinear identities.
Furthermore, we could construct $\mathit{putative}$ partition functions for
these theories based on these bilinear pairings, which could have a range of
lattice interpretations. We also present and discuss modular
re-parameterization of MLDE and their solutions for Fricke groups of prime
levels.
