First of all, it's not magnification that determines whether you can see Jupiter's moons: it's aperture (diameter of main lens or mirror). The same is true in general in astronomy: aperture wins!
There are two problems with Jupiter's smaller moons. First, they are small, so don't reflect much light. Secondly, they are close to one of the brightest objects in the sky, so tend to be washed out by Jupiter's brilliance. So you need a large aperture to even see the tiny specks of light, and then good quality, high contrast optics that won't be overwhelmed by stray light from Jupiter.
The Galilean moons range in brightness from 4.6 to 5.6 magnitude. The next brightest moons are Amalthea (14.1) and Himalia (14.6). Stars of magnitude 14.1 to 14.6 require at least an aperture of 250mm (10-inch) to be visible, and even then they require perfectly dark skies, high magnification, and a trained eye. Amalthea orbits very close to Jupiter, 181,400 km as compared to 421,800 km for Io, so it will be completely overwhelmed by Jupiter except in the largest telescopes. Himalia orbits much farther away, 11,461,000 km, nearly 10 times farther than Callisto (1,883,000 km). As a result, Himalia is the most frequently observed non-Galilean moon. All the other moons of Jupiter are 16th magnitude or fainter, making them very difficult to see visually. Most have been discovered photographically.
My friend Alan Whitman has observed Himalia with a 400mm (16-inch) Newtonian. (RASC Observer's Handbook 2011, p.230).