  It is now well understood that Ward identities associated to the (extended)
BMS algebra are equivalent to single soft graviton theorems. In this work, we
show that if we consider nested Ward identities constructed out of two BMS
charges, a class of double soft factorization theorems can be recovered. By
making connections with earlier works in the literature, we argue that at the
sub-leading order, these double soft graviton theorems are the so-called
consecutive double soft graviton theorems. We also show how these nested Ward
identities can be understood as Ward identities associated to BMS symmetries in
scattering states defined around (non-Fock) vacua parametrized by
supertranslations or superrotations.
