Since you are looking for improvements in the bass the most obvious way to do that is to replace the subwoofer. Problem is that your price range isn't wide enough to make that work for you unless you can find a used subwoofer.
You could use something like this
https://www.minidsp.com/products/minidsp-in-a-box/minidsp-2x4
to use dsp to improve the sound of your Polk.
If you want to make improvements in the rest of the range then replace the satellites with better speakers. You should be able to do that in your price range.