  In this work, we explore the possible existence of several critical endpoints
in the phase diagram of strongly interacting matter using an extended PNJL
model with 't Hooft determinant and eight quark interactions in the up, down
and strange sectors. Besides, we also study the isentropic trajectories
crossing both (light and strange) chiral phase transitions and around the
critical endpoint in both the crossover and first-order transition regions.
