Kyle is the only one I am currently in a time-committed relationship with. This means is that I arrange my schedule first to make sure that I get at least one block of alone time with zir every week, because I feel that this is necessary to maintain the kind of connection I want with zir. Until recently, Abby was also a time-committed relationship and because ze had a more rigid schedule, ze got first pick of time, but I was equally committed to getting that time with each of them (we ended the time-committed aspect because Abby simply didn't have the time or energy, but it is a possibility for the future).
The reason I make some relationships time-committed is that I want to maintain a steady level of intense connection. I want to know everything that happens in their life, I want them to know everything that happens in mine; I want to be completely open, completely known and completely understanding. (not that those are fully reachable but I hold them as goals) That requires a lot of time and energy, so I cannot give it to everyone I love; with the others that I love, I move into intense connection with them when I am with them, but allow gaps in connection.
For me, romantic, sexual, and non-romantic/sexual relationships exist in both time-committed and non-time-committed categories. At this point I am only willing to have time-committed relationships with people who are soulfriends with me (romantic/sexual/neither doesn't matter). Hannah (in Belgium) would also be a time-committed relationship if ze lived nearby, though our relationship is not romantic/sexual, and the same goes for my little sister (in New Orleans), and most likely for Aurilion (in North Carolina) [that one would most likely be romantic/sexual]. I don't have the time or energy required to do time-commitment or soulfriendship over long-distance at this point.
There are some ways that my relationship with Kyle could be considered primary; we don't share finances but we do share and lend money between us often, we live together and intend to keep doing that for as long as we can, we both intend to keep our relationship at its current level of intensity (or more) for the rest of our lives (and I actually do see that happening), and we plan to make ceremonial agreements to each other at some point (and possibly raise children, if the right circumstances line up). But in terms of priority it's different. If there is a case of conflict of priorities for me, whoever has greater need comes first. If I have two lovers who are both in strong need, then they will have to share my person and my space in order for me to be there for them. There is some amount of connection level that enters into that, but usually people will not ask for me to support them unless there is a great need or we're very close. However, Kyle is a very sensitive person, and experiences a lot of crises, so Kyle does generally take more of my support-time than most people would (which has caused conflict with other lovers in the past).
As far as one relationship harming another, I don't prioritize fixing one over the other, but if the only solution is to end one of the relationships, it's going to be the one that is causing more harm (I don't use longevity or role to decide). I'll only maintain relationships that are focused on growth and compassion and provide both parties with sufficient nourishment; my relationship with Kyle tends to be more growthful, compassionate, and nourishing than others so I think it is likely that in a conflict I would end the other relationship, but that is a function of the effect of the relationship, not the role. My goals with my polyness is to maintain conscious choice for that which is growthful, nourishing, and compassionate.