  The SU(2)-Higgs model, with a single Higgs field in the fundamental
representation and a quartic self-interaction, has a Higgs region and a
confinement region which are analytically connected in the parameter space of
the theory; these regions thus represent a single phase. The effect of multiple
Higgs fields on this phase structure is examined via Monte Carlo lattice
simulations. For the case of N>=2 identical Higgs fields, there is no remaining
analytic connection between the Higgs and confinement regions, at least when
Lagrangian terms that directly couple different Higgs flavours are omitted. An
explanation of this result in terms of enhancement from overlapping phase
transitions is explored for N=2 by introducing an asymmetry in the hopping
parameters of the Higgs fields. It is found that an enhancement of the phase
transitions can still occur for a moderate (10%) asymmetry in the resulting
hopping parameters.
