No, you cannot connect a second battery to an audio system without taking away the original battery’s function.
Yes, you can run two batteries one alternator.
There are a few ways to wire dual battery systems. One way is to use an 8-pin Molex connector to wire the two batteries in series. This will create a power connection and allow you to turn on and off the batteries without having to worry about connecting them in the opposite direction. Another way is to use a 3-pin TRS connector to wire the two batteries in parallel.