Cocrystals of Active Pharmaceutical Ingredients (APIs) are an attractive therapeutic alternative to salt formations. However, due to the molecular scale processes involved, the earliest stages of cocrystal formation remain poorly understood. In this paper, some light is shed on the thermodynamics and kinetics of co-crystallization. Importantly, to mimic the molecular scale processes of cocrystal formation, we use 2D Monte Carlo simulations and a computational model with short-range attraction and a mixture of two types of patchy particles (PPs) monomers. Each type possesses four patches, grouped in two by two, and each couple of patches is characterized by its specific placement on the circumference of the monomer and corresponding patch strength (a strong and narrow or weak and wide interaction). The spatial placement of the patches on both PPs monomers (alternating periodically through 60 and 120 degrees and vice versa) selected by us shows the emergence of both rhombohedral (metastable) and trihexagonal (stable) Kagome-like structures. The Kagome-like structures are preceded by formation of two types of trimers involving strong bonds only, or mixed trimers of strong and weak bonds, the later serving as building blocks for the finally generated Kagome patchy cocrystal, after prolonged simulation times. The step-by step process governing the cocrystal formation is discussed in detail, concerning the temperature interval, concentrations of PPs, the specific patch geometry and patch anisotropy as well. It is to be hoped that an understanding of the mechanisms of co-crystallization can help to control practical cocrystal synthesis and the possible phase transformations.