Bioconvection due to the movement of the micro-organism cells is universal and affects many ecological and biological processes, including infection, reproduction, and marine life ecosystems. The impact of the bioconvection is more significant in nanofluids. In the present problem, we investigate the Marangoni triply stratified bioconvective flow of non-Newtonian (second-grade) nanofluid with the presence of motile micro-organisms over a permeable inclined plate. The problem provides an analysis of the impact of second-order effects, namely, viscous dissipation, radiation, and chemical reaction, allowing a set of similarity transformations to convert the governing PDEs into coupled nonlinear DEs. Thereafter, Runge–Kutta Fehlberg's numerical method is employed to find the solution of the DEs for some chosen values of different flow influencing parameters. The impact of crucial parameters on the velocity, temperature, nanoparticles volume fraction, the motile density of micro-organisms, and the quantities of physical interest, namely, local Nusselt number, local Sherwood number, and local motile micro-organism density number are illustrated through the plots and tables. It is revealed that the second-grade fluid parameter indicates a prominent correlation with the Marangoni convection in the bioconvective transport mechanism. Also, the Marangoni convection is significant in bioconvective flows for large Péclet numbers.