Yes I have a female zebra finch and a male society finch and now they have 4 eggs still waiting for them to hatch
Will A Female Zebra Finch And A Male Society Finch Mate?
This is possible and this pairing would even produce hybrid youngsters although these youngsters may not be able to breed when they are older. They would be nice for an aviary though or fostering other youngsters.
I have often heard that a society finch and a zebra finch can hybridize, but I have never seen a bird that anyone could prove was a true cross and I don't believe that it is possible. They are just not closely enough related. Many people will say it is possible, but it always turns out that they just HEARD it is possible and have never actually done it.