Four Galilean moons shadows

Can all four Galilean moons cast their shadows on Jupiter ’s disk at
the same time?

No. A triple shadow transit is as good as it gets (S&T: July 2004, page 94).

The motions of the three inner moons are gravitationally locked so
that, as English astronomer George B. Airy wrote more than a century
ago, “Conjunctions of the second and third satellites [are] always
taking place on the side opposite to that on which the conjunctions of
the first and second take place.” It follows that whenever Io (the
first moon) and Ganymede (the third) are casting shadows on Jupiter’s
face, Europa (the second) cannot do so.

— Roger W. Sinnott