One thing you could do is to just schedule regular dates with one of your partners (maybe the one with the more complicated schedule), and let ones with anybody else you are dating be more spontaneous (with the more flexible schedule). I find having one set date each week with my husband, and one with my boyfriend, leaves me a lot of flexibility in my schedule to make additional plans with either them, or friends, or to take time for myself (I try to schedule Sundays just for me, for instance) etc. When I have more than a few things on the schedule more than a week or two out, I find it incredibly stressful, so that might be useful.
I've never started relationships with two people at the same time, although I have decided against continuing to date somebody once when they were obviously in NRE with a new person they were seeing. Not because I don't think it can't be done, but I'd prefer feeling people aren't distracted by that when I'm getting to know them. So I'm looking forward to reading any responses about that.
Happiness will never come to those who fail to appreciate what they already have.