> if the added mass was solid iron or silicon, so that it would sink to the core, I understand that the solid core would grow. But would the outer gassy layers also grow?

That depends sensitively on "how much" and "what kind of stuff"...but generally electron degeneracy is electron degeneracy. You can't pack too much stuff too tightly or it goes degenerate, and starts expanding outwards into momentum space while shrinking in position space.

The resulting outer gassy layers are tricky, but there's a closely analogous phenomenon in stars: as an old main sequence star fuses up all the hydrogen at its core, it leaves behind a ball of helium "ash" that collapses under its own weight, supported only by electron degeneracy pressure. The central density in our Sun is already very high, about 160x greater than water, but this helium ash ball is closer to 16,000x denser than water. If you could stand on this ball, it would have enormous surface gravity - also meaning fresh hydrogen in a shell surrounding the degenerate helium ball is compressed, and fusion proceeds much more rapidly, expanding the outer layers into a red giant.

In the case of Jupiter, it's still a long way from the pressures / temperatures needed for any fusion, so the gassy layers would just get compressed by the increased density of a more massive, more degenerate core...and that's about it.