  Building on previous work by four of us (ABCN), we consider further
generalizations of Warrington's juggling Markov chains. We first introduce
"multispecies" juggling, which consist in having balls of different weights:
when a ball is thrown it can possibly bump into a lighter ball that is then
sent to a higher position, where it can in turn bump an even lighter ball, etc.
We both study the case where the number of balls of each species is conserved
and the case where the juggler sends back a ball of the species of its choice.
In this latter case, we actually discuss three models: add-drop, annihilation
and overwriting. The first two are generalisations of models presented in
(ABCN) while the third one is new and its Markov chain has the ultra fast
convergence property. We finally consider the case of several jugglers
exchanging balls. In all models, we give explicit product formulas for the
stationary probability and closed form expressions for the normalisation factor
if known.
