Increasing interest has been drawn to optical manipulation of metal (plasmonic) nanoparticles due to their unique response on electromagnetic radiation, prompting numerous applications in nanofabrication, photonics, sensing, etc. The familiar point-like laser tweezers rely on the exclusive use of optical confinement forces that allow stable trapping of a single metal nanoparticle in 3D. Simultaneous all-optical (contactless) confinement and motion control of single and multiple metal nanoparticles is one of the major challenges to be overcome. This article reports and provides guidance on mastering a sophisticated manipulation technique harnessing confinement and propulsion forces, enabling simultaneous all-optical confinement and motion control of nanoparticles along 3D trajectories. As an example, for the first time to our knowledge, programmable transport of gold and silver nanospheres with a radius of 50 and 30 nm, respectively, along 3D trajectories tailored on demand, is experimentally demonstrated. It has been achieved by an independent design of both types of optical forces in a single-beam laser trap in the form of a reconfigurable 3D curve. The controlled motion of multiple nanoparticles, far away from chamber walls, allows studying induced electrodynamic interactions between them, such as plasmonic coupling, observed in the presented experiments. The independent control of optical confinement and propulsion forces provides enhanced flexibility to manipulate matter with light, paving the way to new applications involving the formation, sorting, delivery, and assembling of nanostructures.