  Multi-boson productions can be exploited as novel probes either for standard
model precision tests or new physics searches, and have become one of those
popular topics in the ongoing LHC experiments, and in future collider studies,
including those for electron-positron and muon-muon colliders. Here we focus on
two examples, i.e., ZZZ direct productions through $\mu^{+}\mu^{-}$
annihilation at a 1 TeV muon collider, and ZZ productions through vector boson
scattering at a 10 TeV muon collider, with an integrated luminosity of $10 \,
\text{ab}^{-1}$. Various channels are considered, including, such as $ZZZ
\rightarrow 4l2\nu$ and $ZZZ \rightarrow 4l + 2 \text{ jets}$, etc. Expected
significance on these multi-Z boson production processes are provided based on
a detailed Monte Carlo study and signal background analysis. Sensitives on
anomalous gauge boson couplings are also presented.
