  We address the problem of consistent Campiglia-Laddha superrotations in $d>4$
by solving Bondi-Sachs gauge vacuum Einstein equations at the non-linear level
with the most general boundary conditions preserving the null nature of
infinity. We discuss how to generalise the boundary structure to make the
configuration space compatible with supertanslation-like and superrotation-like
transformations. One possibility requires that the time-independent boundary
metric on the cuts of $\mathscr{I}$ is not fixed to be Einstein, while the
other sticks to Einstein but time-dependent metrics. Both are novel features
with respect to the four-dimensional case, where time-dependence of the
two-dimensional cross-sectional metric is not required and the Einstein
condition is trivially satisfied. Other cases are also discussed. These
conditions imply that the configuration spaces are not asymptotically flat in
the standard sense. We discuss the implications on the construction of the
phase space and the relationship with soft scattering theorems. We show that in
even spacetime dimensions, the initial data compatible with such asymptotic
symmetries produce maximally polyhomogeneous expansions of the metric and we
advance a potential interpretation of this structure in terms of AdS/CFT and
realizations of Ricci-flat holography.
