A method for making a modified polylactide composition, comprising the steps of I. forming a reaction mixture by combining: i) 85 to 99.9 weight percent, based on the combined weight of components i) and ii), of a starting linear polylactide resin or mixture of linear polylactide resins wherein the starting linear polylactide resin or mixture of linear polylactide resins has a relative viscosity of 2 to 4.5_as measured using a capillary viscometer at 30°C on a 1% wt/vol solution of the polylactide resin in chloroform, the ratio of L-lactic repeating units to D-lactic acid repeating units in the starting linear polylactide resin or mixture of linear polylactide resins is >8:92 and <92:8 and the starting linear polylactide or mixture of linear polylactide resins contains carboxyl end groups and ii) 15 to 0.1 weight percent, based on the combined weight of components i) and ii), of a thermoplastic epoxy group-containing polymer having an epoxy equivalent weight of 1000 to 6000, an average of at least three epoxy groups per molecule, a melting temperature of 100°C or lower and a glass transition temperature of 0°C or lower as measured by differential scanning calorimetry per ASTM D-1356-03; II. reacting a portion of the carboxyl groups of the starting linear polylactide resin or mixture of linear polylactide resins with a portion of the epoxy groups of the thermoplastic epoxy group-containing polymer to form a composition that includes a reaction product of components i) and ii) and a quantity of unreacted component i) and III. before, during and/or after step II, melt-blending the reaction mixture or composition formed in step II with iii) at least one branched polyester, wherein the at least one branched polyester has a glass transition temperature of 0°C or lower_as measured by differential scanning calorimetry per ASTM D-1356-03 and constitutes 1 to 60 weight percent of the combined weights of components i), ii) and iii). I. forming a reaction mixture by combining: i) 85 to 99.9 weight percent, based on the combined weight of components i) and ii), of a starting linear polylactide resin or mixture of linear polylactide resins wherein the starting linear polylactide resin or mixture of linear polylactide resins has a relative viscosity of 2 to 4.5_as measured using a capillary viscometer at 30°C on a 1% wt/vol solution of the polylactide resin in chloroform, the ratio of L-lactic repeating units to D-lactic acid repeating units in the starting linear polylactide resin or mixture of linear polylactide resins is >8:92 and <92:8 and the starting linear polylactide or mixture of linear polylactide resins contains carboxyl end groups and ii) 15 to 0.1 weight percent, based on the combined weight of components i) and ii), of a thermoplastic epoxy group-containing polymer having an epoxy equivalent weight of 1000 to 6000, an average of at least three epoxy groups per molecule, a melting temperature of 100°C or lower and a glass transition temperature of 0°C or lower as measured by differential scanning calorimetry per ASTM D-1356-03; i) 85 to 99.9 weight percent, based on the combined weight of components i) and ii), of a starting linear polylactide resin or mixture of linear polylactide resins wherein the starting linear polylactide resin or mixture of linear polylactide resins has a relative viscosity of 2 to 4.5_as measured using a capillary viscometer at 30°C on a 1% wt/vol solution of the polylactide resin in chloroform, the ratio of L-lactic repeating units to D-lactic acid repeating units in the starting linear polylactide resin or mixture of linear polylactide resins is >8:92 and <92:8 and the starting linear polylactide or mixture of linear polylactide resins contains carboxyl end groups and ii) 15 to 0.1 weight percent, based on the combined weight of components i) and ii), of a thermoplastic epoxy group-containing polymer having an epoxy equivalent weight of 1000 to 6000, an average of at least three epoxy groups per molecule, a melting temperature of 100°C or lower and a glass transition temperature of 0°C or lower as measured by differential scanning calorimetry per ASTM D-1356-03; II. reacting a portion of the carboxyl groups of the starting linear polylactide resin or mixture of linear polylactide resins with a portion of the epoxy groups of the thermoplastic epoxy group-containing polymer to form a composition that includes a reaction product of components i) and ii) and a quantity of unreacted component i) and III. before, during and/or after step II, melt-blending the reaction mixture or composition formed in step II with iii) at least one branched polyester, wherein the at least one branched polyester has a glass transition temperature of 0°C or lower_as measured by differential scanning calorimetry per ASTM D-1356-03 and constitutes 1 to 60 weight percent of the combined weights of components i), ii) and iii).