Out of all my dogs, the rat terrier mix seems to be the most inclined to constipate. He got alot less bone than the others to begin with after problems, quickly getting to boneless meals. I cheat too, he and the Jack Russel mix come help me in the barn every day. They kill the mice, I give them a few spoonfuls of fresh goats milk.
Adding a whole egg might fix him up too, just be prepared for mucousy nasty looking undigested egg whites the first time. Kinda lubricates things.
Some of mine don't like to break the yolk and want their egg stirred.