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It is shown that the strange quark mass undergoes a first order transition ina generalized 3 flavor Nambu--Jona-Lasinio (NJL) Lagrangian which includes acomplete set of explicit chiral symmetry breaking interactions. This transitionoccurs in a moderate chemical potential region $\mu \sim 400$ MeV, in additionto the usual chiral transition associated with the light quark sector. Thisfavors the formation of stable strange quark matter at chemical potentialswhich are considerably lower than the ones discussed in the literature. Thereason for this behavior is discussed.

The $T-\mu$ phase diagram of the NJL model in the presence of explicit symmetry-breaking interactions