Johnnycat has it exactly right. You can drag a trailer full of batteries around with you if you want, and you will be able to go longer before you inevitably deplete the batteries. The source of the power is the stator, rated at 550 watts under optimum conditions. Take away the parasitic loads, like the fuel pump, cooling fan, efi, gauge head, tail/brake lights and ignition and you might have 200/250 watts left for "toys". The analogy is that you have a bathtub (the battery) and you are filling it with the tap on low (stator). Once the bathtub is full its full, the rest goes over the overflow. everything is fine until you start using more water from the bathtub than the tap is putting in. Yes if you have a bigger battery (bathtub) it will take linger, but sooner of later you take it all out and you get the battery light or dead battery.
So what do you do to really solve the problem?
Stator rewinds have been popular in the 3 wheeler/quad group for twenty years or so. I havent had a RZR stator in my hands but a guess is that they could probably be rewound for an increase of 50-100% rated output. Fine. The weak link then becomes the regulator/rectifier. A stator system has no way to actually regulate the output of the stator like an alternator, so any excess is dumped across the external regulator. This makes heat. heat is the enemy of anything electronic. Since Polaris already moved the regulator/rectifier to a cooler location, I personally doubt it has much excess capacity. There are other regulators out there that might do the job.
A real alternator. There are kits out there and they arent rocket science. A 60amp alternator will power alot of toys. But even it wont power a 2000watt stereo system. Under optimum conditions at good revs a 60amp alternator is only providing around 900watts, so you are once again draining the bathtub faster than you are filling it. You are also using around 2 of your precious horsepower to do it. While that is an extreme example I think it helps illustrate the point.
One more thing for some of you to consider. If you use a winch on your vehicle. I dont use one, but if I did, I would want it and the battery capacity to be sufficient to retrieve the vehicle (dead) from the nastiest situations. So I would size the battery to provide full winch load for something like 15 or 20 minutes.
