  In this work we revisit the $E_8\times\mathbb{R}^{+}$ generalised Lie
derivative encoding the algebra of diffeomorphisms and gauge transformations of
compactifications of M-theory on eight-dimensional manifolds, by extending
certain features of the $E_7\times\mathbb{R}^{+}$ one. Compared to its
$E_d\times\mathbb{R}^{+},\ d\le 7$ counterparts, a new term is needed for
consistency. However, we find that no compensating parameters need to be
introduced, but rather that the new term can be written in terms of the
ordinary generalised gauge parameters by means of a connection. This implies
that no further degrees of freedom, beyond those of the field content of the
$E_{8}$ group, are needed to have a well defined theory. We discuss the
implications of the structure of the $E_8\times\mathbb{R}^{+}$ generalised
transformation on the construction of the $d=8$ generalised geometry. Finally,
we suggest how to lift the generalised Lie derivative to eleven dimensions.
