The invention relates to thermoplastic compositions comprising a thermoplastic polyamide matrix and at least one additive which modifies the interaction between the matrix and an agent. The purpose of the invention is to provide an additive which modifies the interaction between a copolyamide-type thermoplastic copolyamide matrix and at least one agent. The aforementioned additive, which comprises at least one hyperbranched functionalised polymer, is not compatible with the matrix. Moreover, said additive can be used for the controlled modification of the interaction between the thermoplastic copolyamide and an internal or external chemical agent. Preferably, the composition does not contain hyperbranched polymers which produce therein a reduction in the molar mass of matrix M which is greater than or equal to 7% in relation to a sample composition which comprises matrix M but does not contain hyperbranched polymer additive(s). Said mass measurement is taken preferably using a determined protocol P. The invention is suitable for use in moulding, injection moulding, injection/blow moulding, extrusion/blow moulding, extrusion or spinning.