You would be a lot better off going to a larger battery, or at least a battery "bank", then trying to have a third selection on a battrey switch.
By best recommendation is to use a pair of Golf Cart batteries. These are usually designated as being type "T-105" or "2200". They are are 6 volts each so you will need to connect to in series (plus of one to neg of the other) to get 12 volts. Treat this pair of batteries as just one for the purpose of the battery switch.
Regular "marine" batteries are either "24" (80 amp hours) or "27" series (100 amp-hours). The amp hours are established for a 20 hour rate, so a 27 series would theoretically provide 5 amps for 20 hours. Efficiency drops dramatically as the rate increases, so they may only provide 50 amps for one hour (50 amp-hours).
A golf cart battery is typically 220 amp-hours. Their 20 hour rate would be 11 amps for 20 hours. At 50 amps they would last three hours (the draw as a precentage of their total capacity is not as high so they maintain better efficiency).
I would also recommend that you connect the stereo, or at least the amps, directly to the big battery bank and NOT to the output of the battery switch. Leave the smaller battery for running the engine and starting, use the big deep cycle battery for tunes.
There are a number of different "battery combiners" that you might want to investigate. A battery combiner is essentially an automatic battery switch. It will monitor both side of the switch and if it sees that one battery is getting charge (the voltage is 13.2 volts or higher) it will close the switch and connect the other battery so they both charge.
I would add this in addition to your existing manual battery switch (Perko). Leave the manual switch on the starting battery, not on "BOTH".
With this setup you will have the easist to use and most versitile setup possible. You won't have to remember to operate the battery switch when you start or stop. If your starting battery does crap out on you you can still switch to the deep cycle battery to help get started. The two six volts in series is the least amount of additional wiring (just one short cable to hook the two batteries in series) and it also provides the best bang for the buck (most amp-hours per dollar).