We consider the unification problem over theories that are extensions of ACI or ACUI, obtained by adding finitely many homomorphism symbols, or a symbol `*' that distributes over the ACUI-symbol denoted `+'. We first show that when we adjoin a set of commuting homomorphisms to ACUI, unification is undecidable. We then consider the ACUID_l-unification problem, i.e., unification modulo ACUI plus left-distributivity of `*' over `+', and prove it is NEXPTIME-decidable. When we assume the symbol `*' to be 2-sided distributive over `+', we get the theory ACUID, for which the unification problem remains decidable. But when equations of associativity-commutativity, or just of associativity, on `$*$' are added on to ACUID, the unification problem becomes undecidable.