Optical cavities in the near-concentric regime are not very common due to challenging alignment requirements, but can be useful for observing cavity QED effects exploring strong atom-light coupling due to their small effective mode volume. They have also near-degenerate transverse modes. These features provide an interesting platform to explore multi-mode interaction between atoms and light. Here, we use a spatial light modulator (SLM) to shape the phase of an incoming light beam to match several Laguerre-Gaussian (LG) modes of a near-concentric optical cavity. We demonstrate coupling efficiency close to the theoretical prediction for single LG modes and well-defined combinations of them, limited mainly by imperfections in the cavity alignment. We feel that Optics Express reaches out better to a more optics-oriented audience compared to journals with a focus on quantum information and atomic physics.