  We explore the existence of a class of generalised Laplace maps for third
order partial differential operators of the form
\[\partial_1\partial_2\partial_3+a_1\partial_2\partial_3+a_2\partial_1\partial_3+a_3\partial_1\partial_2+a_{12}\partial_3+a_{23}\partial_1+a_{13}\partial_2+a_{123}\]
and related first order $3\time 3$ systems and show that they require the
satisfaction of constraints on the invariants for such operators.
