Pluto takes about 247.92065 years to orbit the Sun. The study of its cycle is yet to be completed and written up. Though it’s conjunctions aren’t visible to the casual observer, Pluto too seems to have a cycle related to the Jubilee cycle, probably working behind the scenes to help fine tune the precise timing of the cycles of the visible planets, with probably its strongest influence being on the paths taken by Saturn and Jupiter.
Though Pluto will likely be the last Solar System body to be fully investigated here, it should be understood that every Solar System body has some degree of influence on the paths taken by the rest. The question is just how much influence. If we were to look at an individual asteroid, its effect on the paths of the visible planets would certainly be negligible. But I wonder about the asteroids as a group – whether together they might have a perceptible influence on the paths of the visible planets.