I wrote this before I figured out you were talking about multi-way draws, IMO, there isn't much to multi way draws other than determining whether or not you have the + EV to bet or call on the flop and turn, and whether or not you want to lead the pot, steal the pot or AI on the resteal.

This is mostly H2H and raising OP stuff,

When you have a Straight draw that's forfeiting outs to a Flush draw, you can fold, but instead of folding or calling to a 6 outer, you should be more inclined to re-raise.

If you re-raise, you give yourself an opportunity to win the pot with out worrying about the flush on the turn or the flush draw on the river. If your opponent goes over the top, then he's going over the top with high card value, so you're outs are more likely to be live. If he caps with high card value, then you can bluff the flush draw on the turn, which gives you "pseudo outs" to the hand. It's also very likely you've priced out the flush draw, or if the flush draw caps and X hits, you can bluff the flush draw off the hand with "high card" value.

OP,

Check raising with draws is cute H2H, but depending on the board, most of the time it's better to just CBet if you opened the hand from UTG to the Cutoff against the Button and consider whether or not you should double barrel the turn. The biggest advantage to this is that if the draw hits on the turn, it's difficult for your opponent to put you on it. If you bet, it encourages them to bluff the board. If you check, it encourages them to bet out. If you check call, then you can blocking bet bluff the river for value and to set up a re-raise or you can check to encourage them to do something stupid. If its a straight draw, you should be even more aggressive with it, because the odds of the opponent being on a flush draw are a lot higher when he's in position. If it's a flush draw, it actually makes sense for you to slow down when it hits, because that's what TPTK usually does in that position.

More often than not, you should be giving yourself a chance to win the pot with a draw immediately or at least by the turn if you're in position H2H. If you're forfeiting outs, then don't let them buy cards or give them free cards. Most importantly, combine your drawing and your set lines, because people will fold to your draws and pay off your sets more often.
C/Raising is texture and seat dependent, you have to really think about your lines when you do this.