Battery capacity at different loads
If your stereo is running for 12 hours on a set of batteries, you're probably getting about 8 A-h of capacity out of the set, so it's drawing about 660 mA on average. Putting three sets of batteries in parallel would drop the current in each set to about 220 mA, and you'll get something closer to 12 A-h from each set.

In other words, if you just use the three sets sequentially, you'll get 36 hours of playing time (24 A-h total), but if you use them in parallel together, you'll get something closer to 54 hours of playing time (36 A-h total).