Person-based traffic signal timing optimization frameworks have recently been proposed to minimize total passenger delay at intersections. These traffic-responsive frameworks implicitly prioritize transit vehicles over cars due to their higher passenger occupancies while considering conflicts that might exist between transit vehicles arriving from conflicting approaches. However, previous person-based signal timing optimizations consider only fixed phase sequences, which limits their flexibility. This paper extends previously developed algorithms to consider phase rotation in which phase sequences may change within each cycle. The phase rotation is directly incorporated in the mathematical programming framework, but could also be accommodated using an enumeration approach for computational efficiency. The proposed signal timing optimization is tested using numerical simulations of an intersection in State College, PA. The results reveal that phase rotation can reduce overall passenger delay through significantly cutting down bus passenger delay while slightly increasing car passenger delay. However, the performance is sensitive to the assumption made in optimization about phase sequence in future cycles. Assuming a background sequence, rather than an optimized sequence in the current cycle, for future generally results in less frequent phase rotation actions. Such a practice can better maintain a pre-assigned background phase sequence but limits the reduction in passenger delays at the intersection.