The core region of a neutron star may feature quark matter in the color-flavor-locked (CFL) phase. The CFL condensate breaks the baryon number symmetry, such that the phenomenon of superfluidity arises. If the core of the star is rotating, vortices will form in the superfluid, carrying the quanta of angular momentum. In a previous study we have solved the question of stability of these vortices, where we found numerical proof of a conjectured instability, according to which superfluid vortices will decay into an arrangement of so-called semi-superfluid fluxtubes. Here we report first results of an extension of our framework that allows us to study multi-vortex dynamics. This will in turn enable us to investigate the structure of semi-superfluid string lattices, which could be relevant to study pinning phenomena at the boundary of the core. © The Authors, published by EDP Sciences, 2016.