Catalysis of the reaction: N(6)-methyl-L-lysyl(20)- + S-adenosyl-L-methionine = H+ + N(6),N(6)-dimethyl-L-lysyl(20)- + S-adenosyl-L-homocysteine. This reaction is the addition of a methyl group to the monomethlyated lysine residue at position 20 of histone H4, producing H4K20me2.
histone H4K20me methylase activity