I'm afraid that's one of the failings an all in one system has

Unfortunately they offer no upgrade path and you tend to have to scrap/sell and start from scratch if you get frustrated with it's limitations. If you were to remove the sub the satalites will not compensate for the lack of bass and the whole soundstage will be thin and not really what you'd find very desirable.
You may be able to replace the front left/right with better speakers but make sure they are ones that are easily driven since your amp may not cope otherwise.
I feel the best way forward would be to save a while making do with what you currently have and once you have a suitable budget get a seperates system.
Seperates offers you the flexability to upgrade any component at any time and you can get a good budget system these days for very little money
edit :-
I've just looked at the specks of that system and it appears to be 75W which is fairly substantial for an all in one system. You'd probably be able to get away with replacing some of your satelites with bookshelf speakers. Something like the Mission M71i that rs sell for arond £60 a pair may be suitable and give you improved stereo sound.
Does the subwoffer conncet to the ampvia an rca phono cable and is it an active sub? if that's the case you may be able to replace the sub with one that will integrate better.