The effect of conserved baryon, isospin and strangeness charges on the behavior of phase transitions in dense matter is studied. Baryonic matter is described within the three-flavor Polyakov$-$Nambu$-$Jona-Lasinio model and several charge fractions $Y_Q$ are considered. The role of the vector interaction, which can be important to describe dense systems, is discussed. Special attention is given to the case with charge fraction $Y_Q=0.4$, due to its importance in heavy-ion collisions and core-collapse supernova matter. It is shown that the possible formation of chiral-symmetric quark matter in the laboratory will be favored in asymmetric matter. Besides, the inclusion of the vector interaction reinforces the formation of quark matter at lower densities.