  We consider three parties, A, B, and C, each performing one of two local
measurements on a shared quantum state of arbitrary dimension. We characterize
the trade-off between the nonlocality of the Bell correlations observed by AB
and of those observed by AC. This generalizes Tsirelson's bound on the quantum
value of the CHSH inequality, the latter being recovered when C is completely
uncorrelated with AB. We also discuss the trade-off between Bell violations and
local expectation values of observables that anticommute with the ones used in
the Bell test.
