Years ago, we had two older domestic shorthairs that did not deal well with the energy of the Savannahs. Eventually a couple of our friends took pity on them and brought them back to their homes where they are very happy. We get visiting rights...but know that they are better off there. For the first year after we got our first Savannah they were tolerant, but I think after the "kitten" didn't seem to grow up after that first year, they got tetchy and said "no" which to a Savannah means try harder. Then they tried to run away from the Savannahs which of course is an invitation to chase and tackle. We were faced with dividing our house to give them space when the alternative homes offered and we realized that was preferable for our cats.
We now have a British Shorthair, and he does great with them. I did a lot of research, talked to a lot of people...then made my friend Kristine (Gattobello Savannahs) get a Brit to trial first. LOL! The Brit personality is very strong and unflappable. They don't bother to run away, they simply ignore the cat if they don't want to play! It's perfect for the Savannah... and makes a nice contrast in looks and personality. Just they shed buckets of fur... they have the densest fur of the cat breeds and you really notice it in the house...