Biodiesel production from first-generation feedstock has shown a strong correlation with the increase in deforestation and the necessity of larger areas for land farming. Recent estimation from the European Federation for Transport and Environment evidenced that since the 2000s decade, an area equal to the Netherlands was deforested to supply global biodiesel demand, mainly originating from first-generation feedstock. Nevertheless, biodiesel is renewable, and it can be a greener source of energy than petroleum. A promising approach to make biodiesel independent from large areas of farming is to shift as much as possible the biodiesel production chain to second and third generations of feedstock. The second generation presents three main advantages, where it does not compete with the food industry, its commercial value is negligible, or none, and its usage as feedstock for biodiesel production reduces the overall waste disposal. In this manuscript, we present an oligomeric catalyst designed to be multi-functional for second-generation feedstock transesterification reactions, mainly focusing our efforts to optimize the conversion of tallow fat and sauteing oil to FAME and FAEE, applying our innovative catalyst. Named as Oligocat, our catalyst acts as a Brønsted-Lowry acid catalyst, providing protons to the reaction medium, and at the same time, with the course of the reaction, it sequesters glycerol molecules from the medium and changes its physical phase during the transesterification reaction. With this set of properties, Oligocat presents a pseudo-homogenous behavior, reducing the purification and separation steps of the biodiesel process production. Reaction conditions were optimized applying a 42 factorial planning. The output parameter evaluated was the conversion rate of triacylglycerol to mono alkyl esters, measured through gel permeation chromatography (GPC). After the optimization studies, a conversion yield of 96.7 (±1.9) wt% was achieved, which allows classifying the obtained mono alkyl esters as biodiesel by ASTM D6751 or EN 14214:2003. After applying the catalyst in three reaction cycles, Oligocat still presented a conversion rate above 96.5 wt% and as well an excellent recovery rate.