An acid-dyeable polyester composition comprising (a) polyester and (b) secondary amine or secondary amine salt in an amount effective to promote acid-dyeability. The acid-dyeable polyester composition may be prepared by melt blending: the polyester; and polymeric additive prepared from (i) triamine containing secondary amine or secondary amine salt unit(s) and (ii) one or more other monomer and/or polymer units. One polymeric additive comprises polyamide selected from the group consisting of poly-imino-bisalkylene-terephthalamide, -isophthalamide and -1,6-naphthalamide, and salts thereof. Also, the polymeric additive, the blends, shaped articles (e.g., fibers and films), processes of dyeing, and processes for preparing an acid dyeable polyester composition.