IMO, what you're thinking is not possible. In a 2.1 or higher system, the internal circuitry is supposed to divide the audio signals based on their frequency and send the mid high frequency signals to the satellite speakers sends low frequency signals to the sub woofer inside the box.
In case of 2.0 speaker systems, the bass that the sub woofer unit creates is absent and thus to make up with that loss (that creates punch in the audio), the satellite speakers are chosen such that they work up with all the all audio frequencies. But these lack the ability to produce that bass which the subwoofer unit is capable of.
So, IMO, you buying a new 2.0 speaker system won't be able to serve the purpose as the audio will still be loud. I'll suggest either play with somewhat lower volume or move in to a room in the insides of your house as the staircases may be adding to the loud sound effect.