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In this paper, we study the number of ergodic measures of maximal entropy forpartially hyperbolic diffeomorphisms defined on $3-$torus with compact centerleaves. Assuming the existence of a periodic leaf with Morse-Smale dynamics weprove a sharp upper bound for the number of maximal measures in terms of thenumber of sources and sinks of Morse-Smale dynamics. A well-known class ofexamples for which our results apply are the so-called Kan-type diffeomorphismsadmitting physical measures with intermingled basins.

On the number of ergodic measures of maximal entropy for partially hyperbolic diffeomorphisms with compact center leaves