  Studies of black hole superradiance often focus on the growth of a cloud in
isolation, accompanied by the spin-down of the black hole. In this paper, we
consider the additional effect of the accretion of matter and angular momentum
from the environment. We show that, in many cases, the black hole evolves by
drifting along the superradiance threshold, in which case the evolution of its
parameters can be described analytically or semi-analytically. We quantify the
conditions under which accretion can serve as a mechanism to increase the
cloud-to-black hole mass ratio, beyond the standard maximum of about 10%. This
occurs by a process we call over-superradiance, whereby accretion effectively
feeds the superradiance cloud, by way of the black hole. We give two explicit
examples: accretion from a vortex expected in wave dark matter and accretion
from a baryonic disk. In the former case, we estimate the accretion rate by
using an analytical fit to the asymptotic behavior of the confluent Heun
function. Level transition, whereby one cloud level grows while the other
shrinks, can be understood in a similar way.
