The present invention relates to systems and methods of using fatty acid alkyl ester solutions to refine feed stocks before converting the feed stocks into fatty acid fatty acid alkyl esters. In an embodiment, the invention includes a method for producing fatty acid alkyl esters. The method can include mixing a crude lipid feed stock with a refining solution to form a crude product mixture, the refining solution comprising greater than about 10 wt. % fatty acid alkyl esters. The method can include extracting the liquid phase from the crude product mixture to obtain a purified lipid feed stock. The method can also include reacting the purified lipid feed stock with an alcohol to form a product mixture comprising fatty acid alkyl esters. In an embodiment, the invention includes a method of making a fatty acid alkyl ester composition. The method can include extracting lipids from a corn-based ethanol production byproduct, adding an alcohol solution to the lipids to form a reaction mixture, and contacting the reaction mixture with a metal oxide catalyst. Other embodiments are included herein.