  Quantum steering, a type of quantum correlation with unique asymmetry, has
important applications in asymmetric quantum information tasks. We consider a
new quantum steering scenario in which one half of a two-qubit Werner state is
sequentially measured by multiple Alices and the other half by multiple Bobs.
We find that the maximum number of Alices who can share steering with a single
Bob increases from 2 to 5 when the number of measurement settings $N$ increases
from 2 to 16. Furthermore, we find a counterintuitive phenomenon that for a
fixed $N$, at most 2 Alices can share steering with 2 Bobs, while 4 or more
Alices are allowed to share steering with a single Bob. We further analyze the
robustness of the steering sharing by calculating the required purity of the
initial Werner state, the lower bound of which varies from 0.503(1) to
0.979(5). Finally, we show that our both-sides sequential steering sharing
scheme can be applied to control the steering ability, even the steering
direction, if an initial asymmetric state or asymmetric measurement is adopted.
Our work gives insights into the diversity of steering sharing and can be
extended to study the problems such as genuine multipartite quantum steering
when the sequential unsharp measurement is applied.
