  A hybrid Potts model where a random concentration $p$ of the spins assume
$q_0$ states and a random concentration $1-p$ of the spins assume $q>q_0$
states is introduced. It is known that when the system is homogeneous, with an
integer spin number $q_0$ or $q$, it undergoes a second or a first order
transition, respectively. It is argued that there is a concentration $p^\ast$
such that the transition nature of the model is changed at $p^\ast$. This idea
is demonstrated analytically and by simulations for two different types of
interaction: the usual square lattice nearest neighboring and mean field
all-to-all. Exact expressions for the second order critical line in
concentration-temperature parameter space of the mean field model together with
some other related critical properties, are derived.
