the factory subwoofer is 8"..... so putting in a 10" would require you to modify the opening on the box. i actually learned how to gain access to it last night (yea i was bored) and it's actually quite easy to get to.

now i have no clue about the whole wiring setup.

 

The stock sub is limited by its size, wattage, size of the enclosure, and the stock amp. You can improve on any of those depending on how much work, money and space you want to sacrifice.
If you just replace the 8" sub driver with a different brand, I dont see it making much of a difference. I think it only gets about 60watts or so, so the amp is the real limitation. You could try adding a more powerful amp to the stock sub, but Im not sure how much it would take before damage occurs.
If you want more bass, adding a mono amp with a higher wattage sub will do it. Enlarging the opening to take a 10" would make a good improvement also, as there are shallow 10" that would fit, maybe not optimal in that small an enclosure, but it will work.
As for wiring, you could probably use the subwoofer wires coming out of the stock amp to attach a line driver or lineout converter, but there could be some kind of processing involved in the factory system that limits the bass output, its been done on other vehicles. The best way is to add an aftermarket deck too, but thats more complicated and expensive. I just tapped the wires from the factory deck and wired to the high level inputs of the amp, again not optimal but when I used a LOC I had alternator whine which could mean other wiring issues.

 

How would I go about adding a second amp to run a new 10" sub? I am really horrible with the audio end of the automotive spectrum. I am looking to spend no more than $300.

 

As someone already said unless you can work with Fs, Vas, Qts, F3, and Xmax simply putting another sub in the OEM box will sound like garbage unless you get REALLY lucky. I've been installing car audio for longer than I'm willing to admit..lol I don't have the OEM sub box so I don't know if it's sealed or ported. I'll assume it's sealed so IF you can figure out the internal cubic feat you can match it to another 8" sub made for a sealed enclosure. I don't like free air subs and trying to port the OEM box would be too complicated unless you really know what you're doing. Plus that OEM amp probably isn't the most efficient thing so I would be careful. I have a 2011 without the Pioneer system. I'm going to buy the PAC AOEM-GM1416A and *hopefully* it will mate up with my factory head unit giving me 2 sets of RCA outs with remote turn on. The battery in the back of the HHR is an installers dream for adding an aftermarket amp and sub. I'll mount a mono amp to a low profile sealed speaker box which should fit in the space between the spare the rear deck. Throw a dynamat trunk kit back there and should be good to go...I hate rattles. A little tip for those that don't know. If your license plate rattles because of the bass. Put some rubber O-rings between the back of the plate and your car. Rubber grommets would be best.

 

Ok, you look like you might know this, I am not far away from having my sub and amp fully installed. Questions I have are:

I have the Pac-Audio 1416a adapter, I'm wondering if the chime sounds pass through the line converter in it or is that introduced elsewhere in the system? I want to keep the chime but do NOT want it amplified if possible. If I have to jimmy rig a small speaker to the system just for the chime I will.

Interior: Is there a good guide somewheres that I can reference for removing the interior of the cargo space to mount the subwoofer as well as a dash tear-down? I haven't been able to locate either one of these information items yet.

Also, I just stuffed some of the poly fill into the stock sub enclosure with the stock sub. Got a Polk Audio PA-330 hooked up with the sub wired series for a 4ohm load bridged on the amp.

Thunder.

Much better response than I would have expected.. the undercarriage rattles, there is definite sub bass emanating away from the vehicle, and I was vibrating part of my house.. Mind you I am now running the sub at likely close to its max levels as I can easily make it popopop if I turn it up just a little more.. I estimate its going somewhere around 100w.. maybe so much as 140.