I'm not so sure about it being possible to modify the modules themselves. I believe that they are pretty fixed.Rogue adds a tube input stage to sweeten the sound from the Class D output stage. This is a good example of adding a house sound.
Definitely possible - Rogue does it.
Boutique amp makers are under a lot of pressure to differentiate their products from the module, which is also branded. Ice has bundled a power supply with the module, leaving "amp makers" scrambling to find tweaks for the copywriters to wordsmith.
Things are changing though. Module makers realize that boutique amp makers want more control so they can impart their house sound. Hypex has a module that they won't sell to DIY.
Anyway, it's interesting to sit on the sidelines and watch a newer market develop inside of our dinosaur hobby. ;-)