That's a decent stand-alone system for what it is but doesn't really lend itself to upgrading for several reasons.
First, that's a "boom box", not a conventional stereo. Upgrade options may be limited.
Second, the specs on that type of equipment is highly exaggerated. IOW that power rating may be at some ungodly high distortion level.
Finally, from looking at your specs, it would appear that your mains are bi-amped, using whatever power is available. Odds are that those two amps were designed specifically for those particular speakers.
Frankly, I'd allocate your funds to getting a receiver and some starter speakers, perhaps two for now. Then when you feel ready, add a center, surrounds, and a subwoofer.