We present a same-path polarization interferometer that uses two spatial light modulators to encode the most general type of Poincaré beam. We demonstrate this design by presenting new results on the encoding of symmetric C-point polarization singularities using spatial modes with high-order topological charges. We also present new results on composite C-points. These are cases where there are multiple C-points in a single beam obtained by combining two modes with composite optical vortices in orthogonal states of polarization. The measurements show good agreement with the simulations.