  We consider orbifoldings of the Moonshine Module with respect to the abelian
group generated by a pair of commuting Monster group elements with one of prime
order $p=2,3,5,7$ and the other of order $pk$ for $k=1$ or $k$ prime. We show
that constraints arising from meromorphic orbifold conformal field theory allow
us to demonstrate that each orbifold partition function with rational
coefficients is either constant or is a hauptmodul for an explicitly found
modular fixing group of genus zero. We thus confirm in the cases considered the
Generalised Moonshine conjectures for all rational modular functions for the
Monster centralisers related to the Baby Monster, Fischer, Harada-Norton and
Held sporadic simple groups. We also derive non-trivial constraints on the
possible Monster conjugacy classes to which the elements of the orbifolding
abelian group may belong.
