  We consider a recently proposed extension of the Bondi-Metzner-Sachs algebra
to include arbitrary infinitesimal diffeomorphisms on a (2)-sphere. To realize
this extended algebra as asymptotic symmetries, we work with an extended class
of spacetimes in which the unphysical metric at null infinity is not universal.
We show that the symplectic current evaluated on these extended symmetries is
divergent in the limit to null infinity. We also show that this divergence
cannot be removed by a local and covariant redefinition of the symplectic
current. This suggests that such an extended symmetry algebra cannot be
realized as symmetries on the phase space of vacuum general relativity at null
infinity, and that the corresponding asymptotic charges are ill-defined.
However, a possible loophole in the argument is the possibility that symplectic
current may not need to be covariant in order to have a covariant symplectic
form. We also show that the extended algebra does not have a preferred
subalgebra of translations and therefore does not admit a universal definition
of Bondi 4-momentum.
