If I remember correctly, yes, it is possible, but it requires some development work.
I would start with implementing the IServerNotify interface, override public void onServerInit(IServer) and use something along those lines (far from functional example:)
List VirtualHosts = VHostSingleton.getVHostNames(); // ... list of virtual hosts
IVHost vhost = VHostSingleton.getInstance(VHostName); // get vhost instance
Stream s = Stream.createInstance(vhost, AppName, StreamName); // create stream name (this is your "1 output stream")
s.play(FileName, 0, -1, true); // just play something, in my case its a video clip
I'm sure there are better examples if you search around the forums. All I'd have to do with above is figure out how to stream live stream sources and how to control the streaming. That, I hope, should be possible ;)
The most important function for this is Stream.play. You will probably call this when ever you want to change the input for this output stream that is created.
If you know exactly what sequence you want to stream, you can just use the scheduler, the first link. If you want to be able to switch dynamically in any way you will have to have a controller of some type, most likely a Flash RTMP application that one person will operate to modify the stream that everyone can see. That is quite involved but there is a starting place in this example: