  In light of the recently discovered $W$-boson mass anomaly by the CDF
Collaboration, we discuss two distinct mechanisms that could possibly explain
this anomaly through the introduction of high-dimensional $SU(2)_L$ scalar
multiplets. The first mechanism is the tree-level $W$-boson mass correction
induced by the vacuum expectation values of one or more $SU(2)_L$ scalar
multiplets with odd dimensions of $n\geq 3$ and zero hypercharge of $Y=0$ in
order to avoid the strong constraint from measurements of the $Z$-boson mass.
The second mechanism is to consider the one-loop level $W$-boson mass
correction from a complex multiplet. In particular, we focus on the case with
an additional scalar octuplet with $Y=7/2$. As a result, we find that both
mechanisms can explain the $W$-boson mass anomaly without violating any other
theoretical or experimental constraints.
