The results of an experiment of pion-induced pion production on 16O at a laboratory energy of 280 MeV are reported. The four-fold-differential cross section, +dΩπ+dEπ+dEπ, was measured, and the missing mass, Mx, for the reaction 16Ofs(π+,π+π−) at laboratory angles of 50°, 80° and 115° for the π−, and from 22° to 128° for the π+ was deduced. The angular and energy distributions of the many-fold differential cross sections are compared with an A(π+,π+π−) model for the reaction. The observed cross sections are reproduced in magnitude and shape when the theoretical calculations consider a proper pion dispersion relation, gw(q), inside the nuclear medium. The total cross section, deduced by integrating the four-fold differential cross sections, is compared with the available theoretical predictions for the 16O(π+, π+π−) reaction.