  We investigate the effect of weak disorder on different coupled $q$-state
Potts models with $q\le 4$ using two loops renormalisation group. This study
presents new examples of first order transitions driven by randomness. We found
that weak disorder makes the models decouple. Therefore, it appears that no
relations emerge, at a perturbation level, between the disordered $q_1\times
q_2$-state Potts model and the two disordered $q_1$, $q_2$-state Potts models
($q_1\ne q_2$), despite their central charges are similar according to recent
numerical investigations. Nevertheless, when two $q$-state Potts models are
considered ($q>2$), the system remains always driven in a strong coupling
regime, violating apparently the Imry-Wortis argument.
