This is what I did for my car, which doesn't have much aftermarket support.
1. Go out to your car and snap a picture of the clearance from the inner wheel to the suspension components, and the outer wheel to the fender. Do this for the front and rear. Here's an example:
You now have a general idea of how much room you have to play with based on the photos.
NOTE: The higher the offset, the more inboard the wheel will sit. So if your RX-8 wheels are 18x8 +50, and you replace them with an aftermarket wheel that is 18x8 +35, the new wheel will sit 15mm further out from the centre of the car (i.e. 15mm further away from the suspension components).
2. Note the specs of your rims and tires.
3. Go to willtheyfit.com and input your current wheel setup and the wheel setup you are considering. The calculator will provide a comparison between the two setups.
4. The comparison provided will include important information like change in wheel diameter. It will also provide a visual representation of your current setup and your potential setup. Compare that with the photos you took to get a good idea of whether the wheels will fit. It isn't exact, so if you're working with a much smaller amount of clearance, unfortunately you'll have to rely on the experience of others, or worst case scenario, trial and error.