In several biotechnological processes, multiple slips are the most paramount, such as blood pumping from the heart to different body components, endoscopy treatment, pabulum distribution, and the heat transport phenomenon regulation. In the current research, we have studied the multiple slips, Darcy–Forchheimer, and Cattaneo–Christov heat flux model on a stretching surface exposed to magnetic carbon nanotube nanofluid. We have additionally included a heat source or sink, a chemical reaction for manipulating the heat and mass transport phenomena. The resulting governing partial differential equations have been transformed into ordinary differential equations. With the Runge–Kutta–Fehlberg fourth–fifth‐order procedure, the transformed governing equations are numerically solved. Numerical solutions for different parameters for velocity, temperature, and concentration profiles (Eckert number, velocity slip, thermal slip, mass slip, etc.) are highlighted. Graphical and numerical results for the various parameters in the modeled problem have been outlined. The present numerical results are compared with the published ones for some limiting cases. The slip has been found to control the flow of the boundary layer.