Histone methyltransferase that specifically di- and trimethylates 'Lys-20' of histone H4 (H4K20me2/me3). H4 'Lys-20' trimethylation represents a specific tag for epigenetic transcriptional repression. Contributes to dosage compensation of X chromosome-relative to autosome-linked gene expression, possibly by converting H4K20me1 to H4K20m2/me3 on autosomes. Involved in the regulation of growth and body fat metabolism downstream of the TOR complex 2 pathway. N(6)-methyl-L-lysyl(20)-[histone H4] + S-adenosyl-L-methionine = H(+) + N(6),N(6)-dimethyl-L-lysyl(20)-[histone H4] + S-adenosyl-L-homocysteine N(6),N(6)-dimethyl-L-lysyl(20)-[histone H4] + S-adenosyl-L-methionine = H(+) + N(6),N(6),N(6)-trimethyl-L-lysyl(20)-[histone H4] + S-adenosyl-L-homocysteine Belongs to the class V-like SAM-binding methyltransferase superfamily. Histone-lysine methyltransferase family. Suvar4-20 subfamily.