My twins were moved to their own room when they started moving more at night, which was (I think, many years have passed) 3 months. They would nurse to sleep at the start of the night. One baby would wake up at some point, we'd get both up to nurse. They'd be put back in their own bed, until the next go 'round, hopefully in the morning. After a while of this, I started only getting the baby that was actually awake, and nurse in my bed side-lying. Upon hearing the next baby, I transferred the first one to my husband's chest, and I'd get the second one. Most mornings we awoke with two babies in our bed.
With little sister, she slept in a pack and play in our room for a long time, but also had a crib set up in the other room. Usually, once she moved out of our room the first time (not sure when-- probably 4-5 months), she'd start the night in her bed in the other room. Upon waking, she was brought to my bed to nurse side-lying. if I could sleep next to her I would, if not, I'd move her to the pack and play (in my room) or her crib in another room.
Once I realized that bed sharing didn't have to be all night every night, it makes what we do less weighty. Even though my babies all had their own sleep space, and used it, I still consider myself a co-sleeping, bedsharing parent. Our cosleeping just started at the first waking. Doing it this way also affords a few benefits: The transition to a child sleeping more of the night in his own bed begins by returning the child to his own space, rather than bringing into mine all the time. It also allows for a time of adults-only time in my room, which helps us in terms of intimacy. It also allows me to have my moments when I say to an older child "no, I need to sleep soundly. you can't come in yet." Or, as we've trained our older kids, don't try to open a locked door. A shut door means return to your bed. An open door means you can come in and snuggle.