  We present an extension of the framework introduced in [1] to treat
multicomponent systems, showing that new degrees of freedom are necessary in
order to obtain the desired boundary conditions. We then apply this extended
framework to the coupled Gross-Pitaevskii equations to investigate the ground
states of two-component systems with equal masses thereby extending previous
work in the lowest Landau limit [2] to arbitrary interactions within
Gross-Pitaevskii theory. We show that away from the lowest-Landau level limit,
the predominant vortex lattice consists of two interlaced triangular lattices.
Finally, we derive a linear relation which accurately describes the phase
boundaries in the strong interacting regimes.
