A caller reports an emergency requiring multiple emergency services by dialing 999. They explain this to the operator. How do they know which control room to connect the call to first before either they relay the details onto the other services or pass the caller back to the operator so that they can connect the caller onto the other services? Should the control room pass the caller back to the operator then how do they determine the sequence of control rooms that the caller will need to speak to?
You can't.
The way it works with the main three is thus:-
First rule: if something is on fire, you want the Fire Brigade regardless of anything else. If not go to the second rule.
Second rule: if someone is seriously hurt or ill, you want an ambulance regardless of anything else other than the first rule. If not go to the third rule. Exception to this rule would be if a major crime is presently ongoing such as a terrorist attack where controlling it may take priority over medical help to those already injured.
Third rule: you want the Police, or something else they dispatch such as mountain rescue.
Having picked the "main" service they can go on to request any of the others should they also be necessary, e.g. if you ring for an ambulance for a car crash which is blocking the road they'll also sort the Police (or HATOs) to deal with that part, or you ring for the fire brigade they'll request an ambulance as well if you report someone is trapped as odds on they'll need it once they have been got out.
It is a bit odd, and I've long taken the view that there should be a single network of call centres to which you describe what has happened rather than requesting a service and they dispatch what is needed.