Multi-acid polymers are produced having the formula R—SO2—NH—(SO3−H+)n or R—SO2—NH—(PO3−H2+)n and made from a polymer precursor in sulfonyl fluoride form or sulfonyl chloride form The R is one or more units of the polymer precursor without sulfonyl fluoride or sulfonyl chloride, n is one or more, and the multi-acid polymer has two or more proton conducting groups. A method of making the multi-acid polymers includes reacting an amino acid having multiple sulfonic acids or phosphonic acids with a polymer precursor in sulfonyl fluoride form or sulfonyl chloride form in a mild base condition to produce the multi-acid polymer having two or more proton conducting groups.