Can an airline ever simultaneously be a member in good standing of more than one airline Alliance? So far, I've not seen overlap between members of Oneworld, Star Alliance, and SkyTeam--the only Official Airline Alliances I'm aware of.

One thing that threw me for a loop recently, though, is that some airlines seem to participate simultaneously in more than one airline Loyalty Program (LP). And some airlines seem to offer membership in their own LPs to other airlines.

Some examples of the former:
* Aeroflot is a member of the Flying Blue LP (?) yet also has its own LP named Aeroflot Bonus (if I'm reading things correctly)

Some examples of the latter:
* Lufthansa's Miles & More LP seems to have a handful of other airlines associated with it, including SWISS, LOT, and Croatian.

* Flying Blue (owned jointly by Air France / KLM?) has other associated airlines such as Kenya Airways, Tarom, and Air Europa.

Is what I'm seeing and relating here accurate?

What about Hotel Chains and Brands? Is there simultaneous cross-participation in each other's Loyalty Programs? And could there be a third "category" of LP? One created and not owned / curated / managed by any airline or hotel provider?

Wondering what the boundaries are with Alliances and Loyalty Programs, if there are exceptions to the rule, etc. I know some airlines partner with each other outside the bounds of both Alliances and Loyalty Programs. One example being:

* Hawaiian Airlines, not being in any Alliance, partners with some airlines that themselves *are* members of one of the three major Alliances, e.g. ANA (Star Alliance), AA (Oneworld), KE (SkyTeam). Presuming there are no transitive benefits. Are there?