  We construct a variational ground-state wave function of weakly interacting
M-component Bose-Einstein condensates beyond the mean-field theory by
incorporating the dynamical 3/2-body processes, where one of the two colliding
particles drops into the condensate and vice versa. Our numerical results with
various masses and particle numbers show that the 3/2-body processes between
different particles make finite contributions to lowering the ground-state
energy, implying that many-body correlation effects between different particles
are essential even in the weak-coupling regime of the Bose--Einstein
condensates. We also consider the stability condition for $2$-component
miscible states using the new ground-state wave function. Through this
calculation, we obtain the relation $U^{2}_{AB}/U_{AA}U_{BB}<1+\alpha$, where
$U_{ij}$ is the effective contact potential between particles $i$ and $j$ and
$\alpha$ is the correction, which originates from the $3/2$-body and $2$-body
processes.
