Is this a physical impossibility?

[Christopher Witmer]

I'm going to reveal my ignorance with this question, but, hey, it's the
only way to learn.

I love the tonal qualities of the modern piano, but would it be possible
to design a piano to retain these qualities and yet also be able to
behave more like a fortepiano when required by the demands of certain
period fortepiano pieces (e.g., certain passages in some of Beethoven's
piano sonatas which are hard to play strictly as Beethoven instructed
unless a fortepiano is used). I'm not sure it could be done, or whether
it could be done without sounding really wierd -- an animal that
sometimes barks like a dog and sometimes mews like a cat. And for all I
know, if it can be done somebody is already doing it with some special
pedal/damper/stringing implementation.