The standard 88 keys is a very good range for a piano. It's difficult to get a clean, audible and musical tone above the top note (C8), and some pianos struggle to produce a nice sound on the top 3 or 4 notes, anyway. Stewart in Australia makes a very large and expensive grand piano with notes higher than the standard C8, and they've managed to pull it off nicely with clean tones you can hear. Some Bosendorfer pianos have extra bass notes below the standard A0. But these notes are so low, they are more of a rumble than a tone you can discern. It's still very cool, especially if playing octaves with a higher note, and with the dampers lifted, these lower strings can add some interesting resonance to the overall sound of the piano.
What's more important to mention is that on the lower bass notes, even on a standard piano, the fundamental frequency is barely audible, if at all. When you play a low bass note on the piano, you aren't just hearing the fundamental tone, but a whole partial series of higher frequencies produced by the vibrating string: the fundamental, one octave above the fundamental, a fifth above that, a fourth above that, and a series of smaller intervals that get smaller as you progress higher. The amplitudes of the higher partials tend to diminish as you go up, but some are more audible than others.
The tension and hardness/softness of the hammer felt changes the way the hammer excites the strings. Overly bright or hard hammers will excite the higher partials too much, producing a harsh, glassy tone. A properly voiced hammer will have more "give" as it strikes the strings - think of a tennis ball compressing as it hits a wall. There is a lot going on, as you would see with a high speed camera, but to simplify the explanation, a softer hammer with more "give" will be in contact with the strings for a longer duration, which somewhat mutes those higher partials before the hammer bounces back off the strings. When voiced correctly, this "give" produces the more pleasant, musical tone that we try to achieve when voicing hammers, because the amplitudes of the various partials are in a good balance.
Getting back to answering the original question, you could attempt to extend the range of the piano, but going much further beyond the standard 88 keys will not provide a musical advantage, because the treble notes would just become percussive sounds to most ears, and the lower notes would only be producing tones (via the higher partials) that are already present in the standard range of notes.