S-adenosyl-L-methionine-dependent methyltransferase that catalyzes four methylations of the modified target histidine residue in translation elongation factor 2 (EF-2), to form an intermediate called diphthine methyl ester. The four successive methylation reactions represent the second step of diphthamide biosynthesis. 2-[(3S)-amino-3-carboxypropyl]-L-histidyl-[translation elongation factor 2] + 4 S-adenosyl-L-methionine = diphthine methyl ester-[translation elongation factor 2] + 3 H(+) + 4 S-adenosyl-L-homocysteine Protein modification; peptidyl-diphthamide biosynthesis. Belongs to the diphthine synthase family.