Pass both ways
To change how the players interact, simply alternate which way you pass the cards each round.
In rounds 1 and 3, pass each hand to the left.
In round 2, pass each hand to the right.
This variant features a third "dummy" player that alternates between players.
Deal 3 players worth of cards (3 hands of 9).
Put the dummy player's cards face down between you as a draw pile.
Choose one player to be the first to control the dummy player.
When you're in control, draw the top card from the dummy pile and add it to your hand.
Then choose 1 card for yourself and 1 for the dummy player (Your opponent plays 1 card as normal).
Reveal cards and then switch hands, leaving the dummy pile in place.
Now your opponent controls the dummy player by drawing from the pile and then choosing 1 for themself and 1 for the dummy.
Take turns controlling the dummy pile until all cards are played out.
Play 3 rounds as described above, scoring as per normal rules.