Oh man I love these companies. Not only do they provide a manual but they also provide service guides with all sorts of good information - something you won't find from Power Wheels. Anyway The vehicle you have is a Rollplay 6v Chevy Tahoe Fire Rescue. See below for the link to the website that has spare parts and both the manual and service guide. What you'll want to do is check out page 24 of the service guide as there's a wiring diagram to help you out. From what I've seen with Rollplay ride-ons is you can jump up to 12v however you'll need to change out the 6v relays on the PCB board with 12v 30a/40a relays and I'd recommend adding a 30a fuse too. You'll also want to go with an aftermarket battery as the stock battery has a self-resetting fuse that will trip after 10 minutes of use. What I don't know is how well the 2nd controller for the speakers and megaphone will react. You might be okay with 12v but the diagram in the service guide will help you navigate the wiring if you do decide to isolate the sound board.
A 2nd motor: From page 14 of the service guide you'll see that the gearbox and motor are sold as a single assembly - for $15 no less. You can follow the instructions backwards on how to remove the gearbox for adding the gearbox on the other side. What I can't tell you is if both rear wheels have the drive hub on the inside of the tire. I think they do and if that's the case that's great because you won't have to buy the hub/wheel.
Now comes the part where you wire up the motors. The first thing to know is you'll want to wire the motor in reverse polarity compared to the existing motor. This is to make sure they both go in the same direction. Don't worry if you get it wrong you'll know right away and can swap them on the spot. This is why I like to test things first before soldering the wires on though I suppose you can always use quick disconnects if you wish and just swap the leads if you do get them wrong.
The next thing you have to ask yourself is whether to wire the motors in series or parallel? If wired in series the 12v output will be shared between the two motors - they'll each get 6v. In theory this will double your drive time but won't increase speed though you'll probably get a slight speed boost anyway since there would be less drag on the motors. Option two is to wire them in parallel. If wired in parallel both motors will receive the full 12v. In theory this doubles the speed but won't increase your drive time. Unfortunately this ride-on doesn't have a two speed option though you could make one with a high current DPDT switch. What it would do is switch between a series and parallel configuration to the motors. I can make you a wiring diagram if you're interested.