S-adenosyl-L-methionine-dependent methyltransferase that catalyzes the trimethylation of the amino group of the modified target histidine residue in translation elongation factor 2 (EF-2), to form an intermediate called diphthine. The three successive methylation reactions represent the second step of diphthamide biosynthesis. 2-[(3S)-amino-3-carboxypropyl]-L-histidyl-[translation elongation factor 2] + 3 S-adenosyl-L-methionine = diphthine-[translation elongation factor 2] + 3 H(+) + 3 S-adenosyl-L-homocysteine Protein modification; peptidyl-diphthamide biosynthesis. Homodimer. Belongs to the diphthine synthase family.