  This paper is the second of a series that investigates the stochasticity and
degeneracy problems that hinder the derivation of the age, mass, extinction,
and metallicity of unresolved star clusters in external galaxies when
broad-band photometry is used. While Paper I concentrated on deriving age,
mass, and extinction of star clusters for one fixed metallicity, we here derive
these parameters in case when metallicity is let free to vary. The results were
obtained using several different filter systems ($UBVRI$, $UBVRIJHK$,
GALEX+$UBVRI$), which allowed to optimally reduce the different degeneracies
between the cluster physical parameters. The age, mass, and extinction of a
sample of artificial star clusters were derived by comparing their broad-band
integrated magnitudes with the magnitudes of a large grid of cluster models
with various metallicities. A large collection of artificial clusters was
studied to model the different degeneracies in the age, mass, extinction, and
metallicity parameter space when stochasticity is taken into account in the
cluster models. We show that, without prior knowledge on the metallicity, the
optical bands ($UBVRI$) fail to allow a correct derivation of the age, mass,
and extinction because of the strong degeneracies between models of different
metallicities. Adding near-infrared information ($UBVRI$+$JHK$) slightly helps
in improving the parameter derivation, except for the metallicity. Adding
ultraviolet data (GALEX+$UBVRI$) helps significantly in deriving these
parameters and allows constraining the metallicity when the photometric errors
have a Gaussian distribution with standard deviations 0.05 mag for $UBVRI$ and
0.15 mag for the GALEX bands.
