Aikido Mt. Airy and Kinokawa Ryu practice randori constantly, and it only gets more difficult as you get higher rank. Although we have thrown some first day students into the mix, we don't require students to perform this until their second test (5th kyu).
Our definition of randori is "chaos practice", which is almost always multi-person defense. We also have turn-and-throw randori and technique randori. During tests, we require students to do turn-and-throw practice which is moving, turning your hips, and evading your attackers. Students are required to go for a while. (This is usually joked around by saying, "You keep going until the Sensei or Sempai [who is sitting down giving the test] gets tired watching you."
) After they are good and tired, they are required to do one attack and one throw for all for all of the uke's involved. If the Sempai or Sensei giving the test doesn't think the throw was good enough, the uke gets up and attacks again.