I am curious what you mean by 2 compatible breeds? And what breeds you consider incompatible?
Mostly size and level of activity etc. We have a large Golden. He is not overweight just a large build type not one of the smaller field types. I love little Yorkies but I would be worried that the little dog would get injured if they were playing. He's a gentle job but is pretty active. I can't see a Bichon Frise, teacup dog working. For logistics we don't want another large dog. So for small to medium sized dogs we have decided on a Corgi. We adore them too. Corgi's are active, pretty tough and a good size.
To the poster with the dog who would not accept it after three different tries, may I ask what happened?
I've been advised to keep the food separate with Goldens not just because of food guarding but because Goldens eat everything so fast and Corgis can be picky so the Corgi would never get any food. I've heard from lots of Golden owners that they are pretty accepting of new dogs but I'm still concerned.
A Corgi is over $1K so its an expensive mistake but I hate the idea of not adding a second dog that we really all want if its more likely to work out.