Catalyzes the methylation of 5-carboxymethoxyuridine (cmo5U) to form 5-methoxycarbonylmethoxyuridine (mcmo5U) at position 34 in tRNAs. Four tRNAs (tRNA(Ala1), tRNA(Ser1), tRNA(Pro3) and tRNA(Thr4)) are fully modified with mcmo5U in stationary-phase E.coli. Also present at low frequency in tRNA(Leu3) and tRNA(Val1). 5-carboxymethoxyuridine(34) in tRNA + S-adenosyl-L-methionine = 5-methoxycarbonylmethoxyuridine(34) in tRNA + S-adenosyl-L-homocysteine Expression is positively regulated by H-NS. Belongs to the class I-like SAM-binding methyltransferase superfamily. CmoM family.