
In my breed that only need to eat what is advised for a dachs, when having weight issues substituting veg seems the only way to go, as otherwise cutting the food down means the dog just scavenges when on walks.
Food is bulked out with cooked or raw Carrot, green beans, pumpkin (unsweetened easy to get in the US), any of the squash or marrow family (though a bit pricey unless you grow your won). some people use cooked cabbage, but that can make them windy.
The veg can be used with their good quality (not diet) dry food, or meat and bone.