Presumably you are assuming that with any primary relationships there is a hierarchy in place. While that may be so in a lot of cases, there are quite a few people for whom having a primary doesn't automatically make it a hierarchy.
Primary means that you are living together, and sharing day-to-day life decisions - it doesn't mean automatically that they are "number one and all others are number two... or lower" (loved that movie!).
OK, that having been said, what I interpret you are saying is that you don't want to live with any of your partners, but want to have loving, meaningful relationships with them, still. Am I getting that right?
I think that in a lot of ways this is going to be easier than having primaries, because you can arrange your own schedule a lot easier. The only issue that I can see is, even if someone isn't a cowboy, what happens if you fall in love with them so hard (and they with you) that you decide that you want to move in together, even while keeping everyone else in your life. If that is a boundary for you, then I think that as long as you make that very plain to folks up-front that this isn't on the table, they can make their own decisions.
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