  The superradiant instability modes of ultralight massive vector bosons are
studied for weakly charged rotating black holes in Einstein--Maxwell gravity
(the Kerr--Newman solution) and low-energy heterotic string theory (the
Kerr--Sen black hole). We show that in both these cases, the corresponding
massive vector (Proca) equations can be fully separated, exploiting the hidden
symmetry present in these spacetimes. The resultant ordinary differential
equations are solved numerically to find the most unstable modes of the Proca
field in the two backgrounds and compared to the vacuum (Kerr black hole) case.
