  We show that there is a set of transformations that relates all of the 24
dimensional even self-dual (Niemeier) lattices, and also leads to non-lattice
objects that however cannot be interpreted as a basis for the construction of
holomorphic conformal field theory. In the second part of this paper, we extend
our observations to higher dimensional conformal field theories build on
extremal partition functions, where we generate c=24k theories with spectra
decomposable into the irreducible representations of the Fischer-Griess
Monster. We observe interesting periodicities in the coefficients of extremal
partition functions and characters of the extremal vertex operator algebras.
