A good sub and amp is definitely next.
Whether you listen to drum n bass or classical music, both (and eveything in between) have low notes that dash and door speakers struggle to re-produce.
Think of every speaker being good at a specific task (range of frequencies) and you will understand that, asking a 4" co-axial speaker (for example) to reproduce a full range of frequencies is a bad idea. Give each speaker a specific job to do, and they work much better (and harder)
So, by adding a sub and amplifier to your set up, no only will you be able to start reproducing notes you currently can't (ie, improve the quality by being able to produce a broader spectrum of frequencies) but by stopping the need for your existing speakers to try and produce these notes (ie, by filtering the lows away from these speakers) you will not only improve the quality of their sound but be able to drive them harder, before they begin to croak.
If you give me an idea of your total budget (including cabling etc) I can recommend some sub/amp combo's for you