Synonyms for Maximum (same or very similar meaning)
WordNet sense 1 (the largest possible quantity):
upper limitWordNet sense 2 (the greatest possible degree):
utmost, uttermost, level bestWordNet sense 3 (greatest or maximal in degree; extreme):
supremeWordNet sense 4 (the greatest or most complete or best possible):
maximalFrom the ODE community, based on WordNetadd/edit