  Due to the difficulties of finding superconformal Lagrangian theories for
multiple M2-branes, we will in this paper instead focus on the field equations.
By relaxing the requirement of a Lagrangian formulation we can explore the
possibility of having structure constants $f^{ABC}{}_D$ satisfying the
fundamental identity but which are not totally antisymmetric. We exemplify this
discussion by making use of an explicit choice of a non-antisymmetric
$f^{ABC}{}_D$ constructed from the Lie algebra structure constants $f^{ab}{}_c$
of an arbitrary gauge group. Although this choice of $f^{ABC}{}_D$ does not
admit an obvious Lagrangian description, it does reproduce the correct SYM
theory for a stack of $N$ D2-branes to leading order in $g_{YM}^{-1}$ upon
reduction and, moreover, it sheds new light on the centre of mass coordinates
for multiple M2-branes.
