Catalysis of the reaction: UDP-glucose + a flavonol 3-O-beta-D-glucosyl-(1->2)-beta-D-glucoside = UDP + a flavonol 3-O-beta-D-glucosyl-(1->2)-beta-D-glucosyl-(1->2)-beta-D-glucoside.
UDP-glucose:flavonol-3-O-beta-D-glucosyl-(1->2)-beta-D-glucoside 2\'\'\'-O-beta-D-glucosyltransferase activity