connection limit across services

Perhaps the easiest way would be to establish an active connection count via an iRule on the virtual hosting the data path:

when RULE_INIT {
  array set ::active_clients { }
}
when CLIENT_ACCEPTED {
  if { [info exists ::active_clients([IP::client_addr])]  } {
    incr ::active_clients([IP::client_addr])
  } else {
    set ::active_clients([IP::client_addr]) 1
  }
}
when CLIENT_CLOSED {
  if { [info exists ::active_clients([IP::client_addr])] } {
    incr ::active_clients([IP::client_addr]) -1
    if { $::active_clients([IP::client_addr]) <= 0 } {
      unset ::active_clients([IP::client_addr])
    }
  }
}

Then applying a limit via an iRule on the initial virtual:

when CLIENT_ACCEPTED {
  if { [info exists ::active_clients([IP::client_addr])]  } {
    if {$::active_clients([IP::client_addr]) > 200 } {
      reject
      log local0. "Rejecting [IP::client_addr], 200 Active connections"
      return
    }
  }
}

Happy testing! (Rules loaded fine with the Editor on v9.1.2, not that that ensures a working solution!)