Anaerobic digestion is a process that can provide both clean energy and environmentally sustainable management of organic wastes. However, dry anaerobic digestion is susceptible to inhibitions and still has technological hurdles that limit its implementation. The study of operational parameters for the treatment of OFMSW in many places of the world is conducted, but the effect of the substrate composition is poorly understood. The present study evaluated strategies to enhance methane production from two different types of OFMSW, provided by two municipalities of Sabana Centro (Colombia), that are distinguished from each other by the presence (Cajicá, W1) and absence (Chia, W2) of meat residues. For both residues, higher methane production was achieved when the lowest substrate to inoculum ratio was used. ACoD with MGW enhanced biogas production with both sources of OFMSW, increasing 61% of production when non-meat residues were used, and always being necessary for production on residues with meat. Fungal pretreatment did not increase methane yields as expected from experiences in other studies due to pH drops and the accumulation of potential toxic inhibitors. In conclusion, as organic waste composition is critical to achieve an efficient dry anaerobic digestion performance, results presented in this work highlights the need to consider how much nature of the substrate influences the process. The findings of this study hold significance for the scientific community working on dry anaerobic digestion. The study presents novel insights into the co-digestion of OFMSW and the pretreatment with the WRF. Furthermore, the results have practical implications for local authorities in Sabana Centro. Based on these findings, policymakers can formulate new source-separation policies, and a dry anaerobic digestion facility can be designed to meet the specific characteristics of the substrates.