White Elephant Online provides various rules & variations you can apply. Here is a brief explainer of the different options, and what they mean.
Style of Play
Stealing is when you must choose whether to take a present (or unwrap a new one) before opening a gift. Swapping (more common in "Yankee Swap" variations of play), is when you first open a gift, and then decide whether to keep it, or swap it with someone else.
When you steal a gift from someone, they now have no gift, and then must decide to steal a gift or unwrap a new one. When you swap a gift, you trade gifts so you both still have a gift. In either case, the stealing/swapping can continue (provided you allow it in the additional rules!)
Play bonus swapping round
If you'd like to extend your game, you can turn this option on. When enabled, once the standard game-play is done (i.e. everyone has a gift), each player will be able to go one more time and choose to either keep the gift they have, or swap it with another player. You'll progress through the players in the same order as the original round. Optionally, at any time during this round you can end the game early if everyone is happy with their gifts.
Allow player #1 to steal again at the end
A common rule is that the person who went first (and thus had the 'worst pick') gets to go again at the very end.
Limit number of steals per round
As mentioned above, when someone is stolen from, they have no gift. Normally they can choose to steal another gift, or unwrap a new one. This pattern can continue within a given round indefinitely, until someone unwraps a new gift, ending the 'round'. This option allows you to limit the number of steals per round, which may help keep play-time down with larger groups.
Limit number of times a given gift can be stolen per game
If there's a popular gift, sometimes it can dominate a game (i.e. everyone wants to steal it!) This is fun, but limiting the number of times the gift can be stolen adds a fun and different dimension to the game. 1) It keeps the gift from being the central focus the whole game. 2) When the gift limit is reached, whoever stole it last keeps it permanently! This also means that people who have higher numbers, while they technically have 'better' numbers, may not be able to steal some gifts that got locked earlier in the game.
Limit number of times a given person can be stolen from per game
This variation means that if a certain person has gotten their gift stolen X# of times, from then on they cannot be stolen from. It can be another way to shorten the game with very large groups, and also add a twist to gameplay.
Regardless of what game rules you decide on for your group, during the actual gift exchange we will make sure those rules are enforced systematically.