Multiplication-homomorphic schemes
Well, there seem to be some restrictions you have:


numbers are 32 bit integers
(several) GB of total data
expansion factor matters


Well, standard ElGamal is probably already close to the best you can get. Maybe ElGamal over elliptic curves would work, which have shorter representations at similar security levels (but then the operations on points are homomorphic, and the function from integers to points will most likely not preserve this property). But in general, it's not going to be any better: Trapdoor functions need this kind of size for each element. And if the original element is just 32 bit, there is this kind of expansion.