  We consider a general class of type-II superconductors which are described by
N complex order parameters (OP), with an overall U(N) symmetry for the energy
functional. In the lowest energy state, each OP adopts its own particular
lattice structure, making the spatial variation of the overall condensate very
complex. We present detailed results for the case N=2. We also treat the limit
N -> infinity, which allows us to resolve a recent controversy, by showing that
all previous studies are fundamentally flawed.

Superconductivity