  We consider coupled nonholonomic LR systems on the product of Lie groups. As
examples, we study $n$-dimensional variants of the spherical support system and
the rubber Chaplygin sphere. For a special choice of the inertia operator, it
is proved that the rubber Chaplygin sphere, after reduction and a time
reparametrization becomes an integrable Hamiltonian system on the
$(n-1)$--dimensional sphere. Also, we showed that an arbitrary L+R system
introduced by Fedorov can be seen as a reduced system of an appropriate coupled
LR system.
