This paper presents a new perspective of beamforming designs in Coordinated Multi-Point (CoMP) downlink systems that are combined with multicast schemes. The beamformer computation is expressed as a joint matrix transformation that can be regarded as an extension of the "Sequentially Drilled" Joint Congruence (SeDJoCo) decomposition. A solution of the proposed joint matrix transformation is devised that takes into account the elimination of the multiuser interference as well as the maximization of the desired signal components. Therefore, it leads to a very effective semi-algebraic solution of beamforming designs for the multicast CoMP downlink, which is evident in the numerical simulations.