Had also in my boat a DC to DC charger, but in my case the charter company already removed the extra battery, so i simply removed it and connected the VHF and GPS, which were on this circuit, to one of the spare circuits in the main panel.
Unless we use different terminology, a multiple stage charger does not mean how many separate battery banks it can charge but rather what is the "algorithm" of charging (i.e - bulk, absorption, float and boost charging).
Whether a charger can charge separately more than one bank would probably be defined and "multiple output charger" (I think Sterling has one such charger).
Personally I do not think you need to have the shore power charger charge the starting battery, and I have it (and also my solar charger) connected only to the house batteries. The starting battery, just like in a car, should never get discharged and routine engine operation (in and out of the marina) should keep it full.
I also do not like those 1,2,both,none switches because someday someone will leave it at BOTH and drain the starter battery, or will switch to NONE while the engine is running and fry the alternator diodes. I simply keep a set of jumper wires for emergency starting from the house battery.
However if the boat is left unused for many months then indeed something needs to be done to maintain the batteries to overcome their self discharge. Assuming the house bank is left connected to shore power (personally I do not like this either) then you could leave the DC to DC charger installed, connect the house battery to its input and the starting battery to its output (the starting battery takes the role of the previous emergency battery).
Anther option, which I used several year ago, is take a small (5W is more than enough) 12V solar panel, and connect it to the batteries. take a separate line to each battery bank with a diode on each line (current will flow from panel to batteries but cannot flow from battery to battery). Since it is a very limited current panel there is no need for a solar charge controller, and it will keep the batteries alive. If the boat is kept ashore then you can also totally disconnect the batteries (when in the water you would like at least the bilge pump connected)