If you define the geometry yourself, you can deform it at will.
I have not yet experimented with loaded models.
Examples from my addons:
https://hofk.de/main/threejs/sandboxthreef/basic%20examples.html
https://hofk.de/main/threejs/sandboxthreef/examplesTHREEf%20r90.html
https://hofk.de/main/threejs/sandboxthreeg/MagicSphereTHREEg.html
https://hofk.de/main/threejs/sandboxthreeg/MagicBoxTHREEg.html (examples 16, 17 react to mouse movements)
Addon. Produces almost infinite many time-varying geometries with functions
added:
The basic geometries of three.js can also be modified.
https://codepen.io/hofk/pen/eWdZMb
in German, but easy to translate
https://hofk.de/main/threejs/skeleton/03_skeleton.html
https://hofk.de/main/threejs/skeleton/03_skeleton_debug.html