NOVELTY - Producing (M1) low sulfur diesel product involves introducing mineral feedstock having T5 boiling point of at least 600 degrees F (315 degrees C); hydroprocessing the mineral feedstock in first reaction zone; fractionating the hydroprocessed feedstock to form diesel boiling range fraction and portion having higher boiling range than the diesel boiling range fraction; mixing the diesel boiling range fraction with biocomponent feedstock in ebullating bed reactor; hydrotreating the mixed feedstock in the bed reactor; and hydrotreating the liquid effluent from the bed reactor in a supplemental reactor.    USE - For producing a low sulfur diesel product (claimed).    ADVANTAGE - The method reduces the fouling impact of the feed; produces diesel fuel product which improves the cold flow properties of the (diesel) fuel product; and is operable with lower grades of biocomponent feeds, such as crude vegetable oils, refined vegetable oils, or refined and bleached vegetable oils.    DETAILED DESCRIPTION - Producing (M1) a low sulfur diesel product involves introducing a mineral feedstock having a T5 boiling point of at least 600 degrees F (315 degrees C); hydroprocessing the mineral feedstock in a first reaction zone under first effective hydroprocessing conditions to cause conversion of at least a portion of the mineral feedstock to diesel boiling range compounds; fractionating the hydroprocessed feedstock to produce a diesel boiling range fraction and a portion having a higher boiling range than the diesel boiling range fraction; mixing the diesel boiling range fraction with a biocomponent feedstock in an ebullating bed reactor, where the biocomponent feedstock is introduced above the catalyst support grid; hydrotreating the mixed feedstock in the ebullating bed reactor under second effective hydrotreating conditions; and hydrotreating the liquid effluent from the ebullating bed reactor in a supplemental reactor under third effective hydrotreating conditions to make a diesel boiling range product having a desired sulfur content specification.