  This note provides an extension of the constructive loop vertex expansion to
stable interactions of arbitrarily high order, opening the way to many
applications. We treat in detail the example of the $(\bar \phi \phi)^p$ field
theory in zero dimension. We find that the important feature to extend the loop
vertex expansion is not to use an intermediate field representation, but rather
to force integration of exactly one particular field per vertex of the initial
action.
