I guess, to be in the relationship but to have a mutual understanding that there's little expectation of doing couple-y things. I'm not sure if it would work; both people would need to be on board with it or one could be offended. But it would be, like, Friday night and don't want to eat home alone? Text the girlfriend and see if she's interested in going out. But similarly if you want to get up early to run Saturday morning, there's no expectation of being a couple just because it's Friday night, and if she texts you, it's ok to say no.
Maybe one or the other people end up frustrated with it, but if it's an option of ending it or trying a different approach, maybe it's an option.
Caveat: I'm very single and probably the last person in the world to give advice.