F5 Monitor with special requirement on a Pool

Or if you wanted to just keep one virtual server, you could do it by iRule and create three separate pools (app1, app2, and app3), all using the same six nodes with your appropriate monitor:

when HTTP_REQUEST {
    if { [HTTP::uri] starts_with "/app1" } {
      pool app1
    }
    if { [HTTP::uri] starts_with "/app2" } {
      pool app2
    }
    if { [HTTP::uri] starts_with "/app3" } {
      pool app3
    }
  }