  Network nonlocality exhibits completely novel quantum correlations compared
to standard quantum nonlocality. It has been shown that network nonlocality can
be shared in a generalized bilocal scenario via weak measurements [Phys. Rev.
A. 105, 042436 (2022)]. In this paper, we investigate network nonlocality
sharing via weak measurements in a generalized star-shaped network
configuration with arbitrary numbers of unbiased dichotomic input $k$, which
includes $n$ branches and adds ($m$-1) more parties in each branch to the
original star network $(n, m=1, k=2)$ scenario. It is shown that network
nonlocality sharing among all observers can be revealed from simultaneous
violation of $2^n$ inequalities in the ($n, m=2, k=2$) and ($n, m=2, k=3$)
scenarios for any $n$ branches. The noise resistance of network nonlocality
sharing with a precise noise model is also analyzed.
