This is how I and a lot of other TP Kitchen painters do it:
Remove all doors from the carcasses, leave the hinge on the carcass, if they are butt hinges I remove completely then refit. You can stack them as Dave 69 suggests while your doing the initial degrease and prep but once you start applying paint, I paint all the frames to the carcasses first and leave to dry, then paint back hinge edge of door, re-hang and proceed to coat both sides of that door. Then repeat with each door, this way they are not in your way and both sides dry at the same time. Once you get to the last door your first one will be dry - repeat for next coat. Yes its a bit of hassle taking off and re-hanging each coat but much easier than having doors everywhere!
Hope this helps