It is shown that a first order transition associated with a jump in the strange quark mass appears in a generalized 3 flavour Nambu--Jona-Lasinio (NJL) treatment of quark matter. The generalization of the Lagrangian displays the complete set of spin 0 interactions at leading and subleading orders (LO and NLO) in $\frac{1}{N_c}$counting, including the recently derived NLO explicit chiral symmetry breaking interactions which are of the same order as the 't Hooft flavour determinant. The parameters of the model are tightly constrained by the low energy characteristics in both the pseudoscalar and scalar meson sectors. The transition occurs in a moderate chemical potential region ($��\simeq 400~\mathrm{MeV}$ for zero temperature) in addition to the usual chiral transition associated with the light quark sector. This feature has at its root the inclusion of the explicit chiral symmetry breaking interactions, which therefore can be seen to act as a catalyst in the production of strange quark matter when compared to the conventional version of the model that takes only into account the 't Hooft interaction in the NLO. It can be traced back to the effect of the interactions which do not violate the Okubo-Zweig-Iizuka rule (OZI), without which the empirical ordering of the scalars ($m_{K^\star}< m_{a_0}\approx m_{f_0}$) is not reproduced.

12 pages, 4 figures (11 subfigures). Revised and extended version. Accepted for publication in Phys. Rev. D