Catalysis of the reaction: 2 mono-beta-D-galactosyldiacylglycerol = alpha-D-galactosyl-beta-D-galactosyldiacylglycerol + 1,2-diacylglycerol.
3-(beta-D-galactosyl)-1,2-diacyl-sn-glycerol:mono-3-(beta-D-galactosyl)-1,2-diacyl-sn-glycerol beta-D-galactosyltransferase activity