Catalysis of the reaction: 3-O-{alpha-D-GlcNAc-(n)-(1->4)-beta-D-GlcA-(1->3)-beta-D-Gal-(1->3)-beta-D-Gal-(1->4)-beta-D-Xyl}-L-seryl- + UDP-alpha-D-glucuronate = 3-O-{(n+1)-(1->4)-beta-D-GlcA-(1->3)-beta-D-Gal-(1->3)-beta-D-Gal-(1->4)-beta-D-Xyl}-L-seryl- + H+ + UDP.
UDP-alpha-D-glucuronate:N-acetyl-alpha-D-glucosaminyl-(1->4)-beta-D-glucuronosyl-proteoglycan 4-beta-glucuronosyltransferase activity