Forwarding is a tool for constructing stabilizers for nonlinear systems. A key step in this design technique is to rind an explicit solution to a partial differential equation (PDE), which may be hard to find-actually, the PDE may even not be solvable at all. In this brief note we show that it is possible to provide an additional degree of freedom for the solution of the aforementioned PDE, hence effectively extending the realm of application of the forwarding methodology. Our contribution is illustrated with the example of an inverted pendulum with a disk inertia.