Access to unused spectrum bands of primary networks requires a careful optimization of the secondary cooperative spectrum sensing, if the transmission powers in the two networks are comparable. In this case the reliability of the sensing depends significantly on the spatial distribution of the cooperating nodes. In this paper we study the efficiency of cooperative sensing over multiple bands, sensed and shared by a large number of secondary users. We show that the per user cognitive capacity is maximized, if both the number of bands sensed by the secondary network as a whole, and the subsets of these bands sensed by the individual nodes are optimized. We derive the fundamental limits under different sensing duty allocation schemes. We show that with some coordination the per user cognitive capacity can be kept nearly independent from the network density.