Spot-on, yet again. I tried to highlight your word "operated" above (not sure if its legible in the final product here). A deep and abiding conversation needs to be had with each partner's CPA and a keen understanding of local and State tax regs is always best, e.g., if one partner is using the aircraft in the course of a business (even as simple as business travel, and thus writing off such travel as a deduction), then doing so might affect the tax status/reporting requirements of the other, "personal-use" partners who may never deduct any such aircraft or operating expenses, etc. Suffice it to say that none of this is impossible, nor disallowed, but my point is it needs to be done in black-letter compliance with the tax man's rules.
Bottom line: the partners really need to have a mutually-agreeable, written understanding about what is allowed and not allowed by way of operating the aircraft because one partner's use of it will always affect the other partners' interests, whether they were the operator or not, especially come tax reporting time (if applicable).
A few other "tip of the iceberg" topics to be considered, and by no means is this exhaustive:
Taxes: Most tax authorities relegate the aircraft property tax issue at the State level to, on average, 1.5 persons who are a) overworked and b) paid in precisely opposite proportion to their workload. So one single person will usually have jurisdiction to figure out upwards of thousands of aircraft registered in his or her State.
Naming the partnership: Don't name your entity after the airplane by make, model or N number. It's just not a good idea.
"Business" of the partnership: be very specific that at no time shall the partnership operate the aircraft in a commercial or business pursuit, i.e. the acts of one partner bind the entirety of the partnership. Consult your favorite knowledgable attorney for what this really means. In the simplest of terms: if you and your partners are merely forming the partnership to tend to the usual ownership and costs associated with owning the aircraft, then you're fine. If there are any business pursuits directly associated with and require the aircraft (such as one partner using the aircraft commercially or instructing others outside of the partnership in the aircraft), then you have a different ball of wax that should be the subject of a different thread. Sticky wicket, indeed, if one partner is a commercial business involving the aircraft***.
Partnerships (LLC formation and membership) specifically: It isn't spoken of very often on here, but the issue of FAA Civil Aircraft Registry regulations and guidelines involving LLCs and other partnerships is very straightforward, but also very detailed and complicated to the uninitiated. Consult your favorite competent aviation title lawyer or aircraft title escrow agent in OKC for further help on this very important step before you choose how to structure your LLC or other partnership. And don't be fooled by thinking you don't have a de-facto partnership just because you haven't formed a formal LLC or other corporate entity; if you and another person own an aircraft together, you have a partnership, full-stop (even your spouse, believe it or not). It just depends on what State you each live in as to how that's treated for tax and property purposes. Look at the options on the 8050-1 for the list of types of ownership the FAA recognizes.
Another "wow, I never knew that" moment: the FAA Registry has its own viewpoint, regardless of what your local law might have to say otherwise, about spousal ownership and registration of aircraft: they're either "co-owners" or "partnerships", unless otherwise stipulated by you when you file your ownership and registration docs with OKC. Don't assume your friends at the Registry have a working understanding of your structure. Chew the FAA Registry's food for them by consulting local OKC knowledgable people first--you'll be better off if you do. Getting these seemingly simple documents and elections wrong at Registry filing can literally be the $2.00 o-ring that causes major headaches later (morbidly, don't leave your estate to figure this out later--it can be a nightmare with no end).
***edited to add that the "partners" comprising the partnership can be any number of legally-recognized "persons" or "entities". The FAA Registry has differing views of this versus most State laws governing partner entities within a partnership. Be wary.