  A sequential steering scenario is investigated, where multiple Bobs aim at
demonstrating steering using successively the same half of an entangled quantum
state. With isotropic entangled states of local dimension $d$, the number of
Bobs that can steer Alice is found to be $N_\mathrm{Bob}\sim d/\log{d}$, thus
leading to an arbitrary large number of successive instances of steering with
independently chosen and unbiased inputs. This scaling is achieved when
considering a general class of measurements along orthonormal bases, as well as
complete sets of mutually unbiased bases. Finally, we show that similar results
can be obtained in an anonymous sequential scenario, where none of the Bobs
know their position in the sequence.
