Using concentration estimates along with the Fountain Theorem and its dual form, we establish the existence of two infinite and disjoint sets of solutions for the following Neumann elliptic system involving critical Sobolev exponents, a Hardy potential, and a concave-convex nonlinearity: where Ω ⊂ RN is a smooth bounded domain containing the origin, with N ≥ 7, α1 + β1 = 2*, β ̅ = ((N-2)2/4,  β =  β ∈ [0, β ̅  – 4), 2* – √(1-β/β ̅ )