Let M be the four-dimensional compact manifold M = T² times S² and let k greater than or equal to 2. We construct a C^____infty diffeomorphism F: M to M with precisely k intermingled minimal attractors A₁,..., A_k. Moreover the union of the basins is a set of full Lebesgue measure. This means that Lebesgue almost every point in M lies in the basin of attraction of A_j for some j, but every non-empty open set in M has a positive measure intersection with each basin. We also construct F:M to M with a countable infinity of intermingled minimal attractors.