  We consider trial wavefunctions exhibiting SU(K) symmetry which may be
well-suited to grasp the physics of the fractional quantum Hall effect with
internal degrees of freedom. Systems of relevance may be either
spin-unpolarized states (K=2), semiconductors bilayers (K=2,4) or graphene
(K=4). We find that some introduced states are unstable, undergoing phase
separation or phase transition. This allows us to strongly reduce the set of
candidate wavefunctions eligible for a particular filling factor. The stability
criteria are obtained with the help of Laughlin's plasma analogy, which we
systematically generalize to the multicomponent SU(K) case. The validity of
these criteria are corroborated by exact-diagonalization studies, for SU(2) and
SU(4). Furthermore, we study the pair-correlation functions of the ground state
and elementary charged excitations within the multicomponent plasma picture.
