A lot depends on how much your trio wake each other up and how similar their sleep needs are. With my three, most of the time, DD and DS2 would sleep through each other crying, but DS3 woke DD up and sometimes even DS2. So, when DD or DS2 have been sick, teething, etc., I have kept their routine the same. With DS3, I have played things a lot by ear. Since he often woke the others up, I would often take him out of the room so the others could sleep.
We have had the three in their own room, but have been willing to take a sick child into bed with us. Usually, I would take the first to wake into the guest room. That way, DH was available if one of the other kids needed a parent. If all three were needing to sleep with a parent, I would sleep with two in the guest room and DH would sleep with one in our bed. If all three needed us at the same time, we generally would end up all in their bedroom so DH and I could switch off who had two kids.
Our biggest issues have been during the transitions from two naps to one and again with dropping the nap. They were ready to drop the third nap at about the same time, but they were ready for the other transitions at very different times. When they dropped from three naps to two, they were in cribs, so I would sometimes let them play in their cribs before naps if two were ready for sleep and one wasn't sure or I would put one down earlier than the others. By the time the transition to no naps started, they were in beds and they would jump into each other's beds and wake each other up if they weren't tired enough to sleep, so I dropped everybody's naps earlier than I wanted and put some to bed earlier on nights when they just couldn't make it to bedtime. We had months of somebody falling asleep on the floor or couch most afternoons to catch some extra sleep, but it was much easier than trying to make them all nap.
Also, we have had massive issues with jumping on beds. We had to take the beds out of the room for a few months and get them used to sleeping well on the mattresses before putting the beds back. We took the bedframes out when the first one strated trying to drop naps and put them back in when I stopped trying to get anyof them to nap in the afternoons and they were too exhausted at bedtime to think about jumping.
Basically, we have found that sleep is one of the places that we have to look very carefully at what each child needs and at the personalities of the three kids and be willing to change things up frequently.
I know this is long. I hope it helps.