We report the existence of multi-peaked vector soliton families in normally dispersive passive Kerr resonators. Through cross-phase modulation between two orthogonal polarization components, each peak becomes tightly interlocked, enabling robust localization of the entire wave packet in defocusing cavities. Analysis using snakes-and-ladder diagrams demonstrates the diversity of these vector soliton families, which include dark/bright multi-peaked solitons, flat-topped solitons, and modulation instability (MI) patterns, among others. Furthermore, stability analysis based on the coupled Lugiato-Lefever equations reveals that specific combinations of parameters can simultaneously sustain a family of stable and stationary vector cavity solitons, whose peak numbers can be continuously tuned by adding appropriate perturbations. These findings significantly expand the scope of soliton dynamics and optical frequency comb generation in driven-dissipative systems, independent of dispersion conditions.