  We investigate asymptotic symmetries in flat backgrounds of dimension higher
than or equal to four. For spin two we provide the counterpart of the extended
BMS transformations found by Campiglia and Laddha in four-dimensional Minkowski
space. We then identify higher-spin supertranslations and generalised
superrotations in any dimension. These symmetries are in one-to-one
correspondence with spin-$s$ partially-massless representations on the
celestial sphere, with supertranslations corresponding in particular to the
representations with maximal depth. We discuss the definition of the
corresponding asymptotic charges and we exploit the supertranslational ones in
order to prove the link with Weinberg's soft theorem in even dimensions.
