Catalyzes the S-methylmethionine (SMM) biosynthesis from adenosyl-L-homocysteine (AdoMet) and methionine. SMM biosynthesis (by MMT1) and degradation (by HMT-1, HMT-2 and HMT-3) constitute the SMM cycle in plants, which is probably required to achieve short term control of AdoMet level. Also able to catalyze the selenium-methylmethionine (SeMM) from AdoMet and selenium-methionine (SeMet). May play a role in phoem sulfur transport; such function is however not essential. L-methionine + S-adenosyl-L-methionine = S-adenosyl-L-homocysteine + S-methyl-L-methionine Optimum pH is 7.2. Homotetramer. Belongs to the class I-like SAM-binding methyltransferase superfamily.