Generalized hypersubstitutions are mappings from the set of all fundamental operations into the set of all terms of the same language, which do not necessarily preserve the arities. Strong hyperidentities are identities which are closed under generalized hypersubstitutions and a strongly solid variety is a variety for which each of its identities is a strong hyperidentity. In this paper we determine the greatest $Reg_{G}$-strongly solid variety of commutative semigroups.