A multi-stage agitation system is used for degumming vegetable oil to increase yield and reduce phosphatides. A high-shear mixing phase, that can include multiple stages, subjects an oil mixed with acid and base to a shear rate of greater than 15,000 s−1 to form a neutralized oil mixture. A low-shear mixing phase is further used to disperse water into the neutralized oil mixture. A separation step can be used to remove the phosphatides from the treated oil to form a degummed oil product.