Qt on X11 with multiple display connections?

I have a need to build a Qt application which will create GUI elements on multiple X11 display connections. To be clear, I am not talking about placing elements on different *screens* of a single X11 server connection. This is a situation in which each monitor is on a different physical machine and, thus, must be managed by different X11 servers.

It looks like Qt has built-in support for separate screens on the same display connection but I have yet to see how you would create and manage events from multiple display connections.

Any pointers or thoughts?
Thanks,
Rob

I don't think Qt supports anything like this.