The spin-orbit interaction is an inherent part of magnetism, which links up the independent world of spins to the atomic lattice, thus controlling many functional properties of magnetic materials. In the widely used 3d transition metal ferromagnetic films, the spin-orbit interaction is relatively weak, due to low atomic number. Here we show that it is possible to enhance and tune the spin-orbit interaction by adding 5d platinum dopants into permalloy (Ni81Fe19) thin films by a cosputtering technique. This is achieved without significant changes of the magnetic properties, due to the vicinity of Pt to meeting the Stoner criterion for the ferromagnetic state. The spin-orbit interaction is investigated by means of transport measurements (the anisotropic magnetoresistance and anomalous Hall effect), ferromagnetic resonance measurements to determine the Gilbert damping, as well as by measuring the x-ray magnetic circular dichroism at the L3 and L2 x-ray absorption edges to reveal the ratio of orbital to spin magnetic moments. It is shown that the effective spin-orbit interaction increases with Pt concentration within the 0%-10% Pt concentration range in a way that is consistent with theoretical expectations for all four measurements.