This paper addresses the problem of describing automorphisms of semigroups of transformations. In [2] we were involved in characterizing all automorphisms of CroisotTeissier semigroups. The semigroups of transformations that belong to this large family generally consist of many-to-one transformations whose restrictions to range sets are oneto- one. Here we consider enlargements of Croisot-Teissier semigroups whose elements, restricted to range-sets, are no longer one-to-one. We show that such semigroups contain a maximal Croisot-Teissier semigroup, which in turn is used to present a complete description of automorphisms of these semigroups. Moreover we describe the Green's relations on these enlargements of Croisot-Teissier semigroups, and show that they are in fact simple semigroups, whose regular elements form a bisimple subsemigroup. We start by recalling the definition of Croisot-Teissier semigroups.