You may have to treat the soil to make it better for the grass and limit the dogs to certain areas while others grow, but it IS possibile!
The key to keeping the grass according to my husband is letting the young grass develope a strong root system and proper fertilization. That way when the dogs zoom around - it isn't easily ripped up.
If you want just GREEN grass and aren't a snob like my hubby, you can try St. Augustine grass. It's like crab grass and grows with runners and is damn near impossible to kill