In this paper, we extend the result of Yan and Yang [16] on equations to an elliptic system involving critical Sobolev and Hardy–Sobolev exponents in bounded domains satisfying some geometric condition. In addition, we weaken the conditions on the dimension N and on the potential {a(x)} set in [16]. Our main result asserts, by a variational global-compactness argument, that the condition on the dimension N can be refined from {N\geq 7} to {N>\max(4,\lfloor 2s\rfloor+2)} , where {0<s<2} and still end up with infinitely many solutions.