Dual methyltransferase that catalyzes methylation of elongation factor 1-alpha (eef1a1 and eef1a2) at two different positions, and is therefore involved in the regulation of mRNA translation. Via its C-terminus, methylates the N-terminus of eef1a1 and eef1a2. Via its N-terminus dimethylates lysine residues of eef1a1 and eef1a2. L-lysyl-[protein] + S-adenosyl-L-methionine = H(+) + N(6)-methyl-L-lysyl-[protein] + S-adenosyl-L-homocysteine N(6)-methyl-L-lysyl-[protein] + S-adenosyl-L-methionine = H(+) + N(6),N(6)-dimethyl-L-lysyl-[protein] + S-adenosyl-L-homocysteine N-terminal glycyl-L-lysyl-L-glutamyl-[protein] + 3 S-adenosyl-L-methionine = 3 H(+) + N-terminal N,N,N-trimethyl-glycyl-L-lysyl-L-glutamyl-[protein] + 3 S-adenosyl-L-homocysteine Belongs to the methyltransferase superfamily.