Canonical bases in excellent classes

We show that any (atomic) excellent class R can be expanded with hyperimaginaries to form an (atomic) excellent class R-eq which has canonical bases. When R is, in addition, of finite U-rank, then R-eq is also simple and has a full canonical bases theorem. This positive situation contrasts starkly with homogeneous model theory for example, where the eq-expansion may fail to be homogeneous. However, this paper shows that expanding an omega-stable, homogeneous class R gives rise to an excellent class, which is simple if R is of finite U-rank.