We consider a practical application of the direct method for finding exact solutions of PDE that requires finding solutions of seemingly more complicated overdetermined systems of PDE. We use some ansatzes (most often it is a generalised symmetry ansatz), and then find reduction conditions for the PDE to be reduced using this ansatz. These conditions in most cases are not easy to solve. However, as they are overdetermined systems, we often manage to find their parametric general solutions. I will present an algorithm to find such solutions using successive application of godograph and contact transformations. For the case of the Schroedinger equation with a general nonlinearity that is invariant under the Galilei transformations, we show that this method does not produce anything more than solutions that can be obtained using the classical Lie symmetry reduction. However, in some special cases we can obtain new exact (parametric) solutions.