When working together, it's great to mix teams up to get more cross-pollination. So try to put people together who don't ordinarily work together every day, so that different perspectives are represented in each team. I'll give examples below for a group of four and a group of nine but you can adapt this for any size.
Four: A B C D
Eight: E F G H I J K L M
Round 1
Pair 1: A & B Pair 2: C & D
Group 1: E, F & G Group 2: H, I & J Group 3: K, L & M
Brainstorm suggestions/solutions/ideas, depending on what you're working on. One person from each group stays with the notes (i.e. A & D or E, I & M), the others form new pairs/groups according to the pattern below (round 2).
Round 2
Pair 1: A & C Pair 2: B & D
Group 1: E, H & K Group 2: F, I & L Group 3: G, J & M
In your new group, sort the brainstorming notes into a mind map. In case you're not yet familiar with mind maps, here's a video tutorial on how to mind map. (It uses a software but you can easily see how you could do the same by hand.)
Round 3
Pair 1: A & D Pair 2: B & C
Group 1: E, I & M Group 2: F, J & K Group 3: G, H & L
Translate your mind map into action steps. Make sure to add the name of who owns the task and a date when the next milestone is due.
If you're thinking of working as a team longer term, I can recommend asana as a great app to help you organise your shared projects.