Hi Jamie,
That thing has proprietary connections on the speakers. Long term goal, replace it entirely with an AVR. Replace the speakers with actual speakers (these home theater in a box combo things come basically with tweeter satellites and a little bookshelf falsely labeled as a sub). This isn't meant to be cheeky, just the reality of it. You could clip off the terminals to your satellites and re-terminate them with banana plugs to use on an amplifer or receiver and keep using them though but they're likely hugely sensitive and take next to no power to get loud. The real issue is likely that the "sub" or whatever is included is just not enough in your room, with its placement, to fill out mids and and upper bass, so it sounds anemic or something. You could keep using it as a DVD player or whatever, by using the HDMI output from it into an AVR as an input. Then the HDMI out from your AVR to a TV. And transplant speakers (or just get new speakers, ideally) to/for the AVR.
Sorry, there's not a lot you can do with these home-theater-in-a-box devices.
Very best,