Automatic matching of teams for a running dinner event

If the concept of a running dinner is new for you, it works as the following:

• We form teams of 2👩‍🍳👨‍🍳
• Each team is assigned one course of a meal (appetizer, main dish, desert)🥪🍜🎂
• Each team is joined by 2 teams for the course they cooked 🤝🍽️🍻
• All teams meet up for an after-party 🪩🥳

Altogether a nice, diverse 3-course menu is created 🍳 You meet 12 people (=2x2x3: 2 teams of 2 people for 3 courses)
It's a lot of fun 😁👌

Manually matching the teams as an organizer is quite tedious, so I want to do I automatically