Sure! It's a little bit complicated and it takes some effort to keep track but it's worth it.
I've used names for people to help minimize confusion.
Everyone picks a number to determine order of picking (as usual).
Everyone, in turn, opens a new gift.
Again, in order, the following cycle happens:
Person whose turn it is, "Suzy", chooses to either keep her gift or steal
If Suzy wants to steal, she puts her gift on the table (or whatever central spot) and steals from Lisa
Lisa can then either take the gift from the table or steal. She steals from Jenny
Jenny can then either take the gift from the table or steal. She steals from Kathy
Kathy is now stuck with the gift on the table.
Play passes to the next (in order) person's turn when any of the following happens:
a) Person whose turn it is chooses to keep their gift instead of stealing
b) Anyone who has been stolen from takes the gift from the table
c) third person gets stolen from in the above cycle and takes the gift from the table
Cycles continue till the highest numbered person takes their round 2 turn.
I differentiate between Rounds which go in the order on the slips of paper, and Cycles which go according to the stealing initiated by the person whose turn it is within the round.
As for the cycles, my norm is third person stolen from ends that cycle, however, if you have a smaller group you may choose to make it second person, or, if you have a very large group, you can up it to fourth or fifth person. Again, the idea is that the more stealing the better, but you also want the game to move along so too much stealing can also be bad.
The hard part is keeping track of where you are in round 2. So I tend to call it out as people are stolen from, like
"Who has #1?"
"Ok, you get the gift on the table. Now, who has the number 2?"
I've been using this way of playing for several years and many games (we play other times through the year) and it works great. But again, I must stress, that someone has to run it and keep track. People do tend to get confused -- they're playing, having fun, thinking about what they want to steal, etc. So one person has to be in charge and make sure to keep it progressing properly.
One more thing I do which is totally optional. When I'm hosting at my house, I throw in an extra gift. That puts two items on the table at all times for the third person in the cycle to choose from when they get stuck with whatever is on the table. At the end of the game, there is that one thing leftover and I draw a name to see who ends up with it. It just adds a little bit extra to the fun of the game and I see it as just another expense of having a party.