Yes, they do seem to get along better the more of them there are. The biggest feeder gatherings are in the morning and again in the evenings when they all show up and take turns getting a drink, and things are so harmonious at these times. I think they must be nesting/sleeping in the nearby trees and the feeders are the first stop in the morning and the last stop at night. I see them coming and going throughout the day too but more staggered and that's when I notice more chasing going on.
I grow most of my flowers from seed, so it's been slow growing enough nectaring flowers. I'm still working on that too!