More Mn in any SS has many detrimental effects to surface quality, fluidity, and folding. An increase in Mn with a comparable increase in Si will solve some of these problems. However, what is your application? If you are using 303SS as is with the higher Mn you will find micro-folds which contain, upon metallurgical confirmation, wustite, Iron Spinel, and Fayalite, among other oxides nearby. (depending on the manufacturing process) The fayalite is very detrimental to corrosiveness, as published from Columbus Laboratories in 1972.
Recent studies by the the american foundry society point to some of the same conclusions, however, I am not sure what you are using this material for. Ingots will contain these defects, rolled will not. Hope this helps.