EDIT: Due to me failing to notice a key element of one of the cards used in the combo below, this review is effectively irrelevant! Thank you to the commenters who called it out and corrected me. So feel free to ignore, or read on for a brief vignette about the perils of hubris or something.
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From Zerogrim's review: "...The last thing to highlight here is you CAN (with some great deal of luck) have 14 doggo's in play at the same time under your control, how you achieve this is left as an exercise for the reader, good luck! (bonus star for anyone who figures out how to get more, no matter how hair brained the method)"
I can getcha 16!
This method works for any 'gator, tho Leo Anderson can skip a step or two via Mitch Brown.
Required: 4P multiplayer.
Each player must have in play:
At least 1 player must have and be able to play Teamwork.
All gators move to the same location.
Play Teamwork.
P1 gives you their Sled Dogs AND their Rod Of Animalism. (Relic Hunter * 2 = 3 Accessory Slots, so you can hold 3 Rod Of Animalism.)
Base Slot + Charisma + 3 Rod Of Animalism = 8 (creature) Ally Slots = 16 Doggo Slots.
P2 & 3 give you their Sled Dogs.
TA-DA! You now have 16 Sled Dogs!
(At this point, if you have an Expensive Sofa in play, you must immediately discard it.)