The examination of gaits and gait changes has been the focus of movement physiology and legged robot engineering since the first emergence of the fields. While most examinations have focused on bipedal and quadrupedal designs, many robotic implementations rely on the higher static stability of three or more pairs of legs. Thus far, however, the effect of number of pairs of legs on locomotion dynamics has not been examined. Accordingly, the present approach aims to extend available theory to polypedal designs and examines how the number of active walking legs affects body dynamics when combined with changing duty factors and phase relations. The model shows that ground force interference of higher numbers of active pairs of walking legs can prevent effective use of bouncing gaits, such as trot, and their associated advantages, such as energy efficiency, because significantly higher degrees of leg synchronization are required. It also shows that small changes in the leg coordination pattern have a much higher impact on the center-of-mass dynamics in locomotor systems with many legs than in those with fewer legs. In this way, the model reveals coordinative constraints for specific gaits facilitating the assessment of animal locomotion and economization of robotic locomotion.