You can have excellent training involving three players:
Drills1:
Objective: Player Movement and ball control (cross and down the line).
Player A is stationed in deuce forehand corner; B and C are on the other side of the court (baseline). Player B will hit all his shots (FH cross court, BH down the line) to the forehand of A player who will alternate his groundstrokes cross court and down the line. Upon a mistake made by B player, B will rotate and C will start the rally cross and down the line. After a set period of time, A will swap his place with B player .. and the drill continues.
The above drill can be mirrored for the ad BH corner also.
Drill 2:
Objective: Hitting the ball under pressure; physical conditioning.
Volleyers A and B stationed at the net; C (baseliner) at the other baseline. C will return all his shots to the volleys of A and B who will move C around the court. After five minutes, players are rotated anti-clock wise.
There are many drills involving three players but it is not possible to list them all.
Playing Games:
1. Two servers, one receiver (King of the Court).
Players A and B are servers but one at a time single court. C is a receiver, the King. The server must win three points in a row to replace the king receiver. However, if the server commits error, he will go back and his partner will start the point on his serve.
This works very well with three players.
2. You can also play doubles 2 on 1. The doubles team will hit all their shots in single player's single court whereas the single player will hit all his shots in the doubles team doubles court.