I've never been in a partnership, but I did lease my helicopter to a school, and have been in a club arrangement before.
If you want, you can post (or send privately) the partnership agreement for review. There are tons of gotcha's there. AOPA has lots of suggestions:
https://www.aopa.org/go-fly/aircraft-and-ownership/buying-an-aircraft/pilots-guide-to-co-ownership/agreement-checklistIt helps to look at a lot of sample agreements to get a flavor for best practices. I looked at several before writing my lease agreement and had it reviewed by an aviation lawyer.
There's a billion things to consider, the following are just the things that popped into my mind first...
IMHO the most important clause is the "defective technique" clause. If someone balls up the aircraft, or even just damages it slightly, you don't want to be on the hook for any part of the insurance deductible or the cost of the repair. That cost should be born by the person who precipitated the loss due to their defective technique. Normal wear and tear does not apply, although if you have a partner who has a heavy hand, i.e. headset jacks always (only) break when he flies, or knobs only come off radios when he flies, then that's an issue that will have to be addressed by the partners.
Another important thing to consider is what process is used to achieve consensus among the partners as to what sort of maintenance is going to happen? You only get a quarter share vote for how your maintenance dollar is being spent. Be prepared to speak up or shell out. Or, vice versa, be prepared to speak up or fly a rat-bird.
Savvy Aviation has a ton of great videos that address this issue. Don't be put off by the apparent length of them. Most are only 30 minutes with a one hour Q&A session at the end. You can bang through most any of them in 20 minutes by playing back at 1.5x speed or judiciously skipping some of the longer winded war stories. I highly recommend them!
Club aircraft get beat on. Leasebacks get beat on. Nobody cares and you can't control them. But a partnership is different. Do the existing partners have SOPs on how the aircraft is to be flown? Is everyone managing the engine the same way? That sort of thing.
Financial commitments: what contractual measures are in place if someone turns into a deadbeat? How are shared finances managed? Is there an LLC?
And, finally, will you get your money's worth? In a typical partnership there are always one or two guys that do 90% of the flying and the others are foolishly subsidizing them. You want to be the former and not the latter. How many hours did the aircraft fly in the last 12 months. How many hours do you think you will fly in the next 12 months?