  The most general large ${\cal N}=4$ superconformal ${\cal W}_{\infty}$
algebra, containing in addition to the superconformal algebra one
supermultiplet for each integer spin, is analysed in detail. It is found that
the ${\cal W}_{\infty}$ algebra is uniquely determined by the levels of the two
$\mathfrak{su}(2)$ algebras, a conclusion that holds both for the linear and
the non-linear case. We also perform various cross-checks of our analysis, and
exhibit two different types of truncations in some detail.
