Observers are used in a variety of control applications. This includes estimating a systems state, system parameters, or fault detection. Systematic observer design is applicable on basis of the observer- or observability normal form. While the former normal form is preferable because of the easier observer design, it exists for a smaller subset of dynamical systems than the latter one. For nonlinear systems the vector field in the observability normal form may possess singularities or may fail a Lipschitz condition. This can sometimes be avoided by embedding the system in a higher-dimensional state space. In this contribution this embedding and its implications are discussed for polynomial multiple input or output systems.