This study explores the dynamical impact of cosmic rays (CRs) in Milky Way-like galaxies using the Rhea simulation suite. Cosmic rays, with their substantial energy density, influence the interstellar medium (ISM) by supporting galactic winds, modulating star formation, and shaping ISM energetics. The simulations incorporate a multiphase ISM, self-consistent CR transport in the advection-diffusion approximation, and interactions with magnetic fields to study their effects on galaxy evolution. Key findings reveal that CRs reduce star formation rates (SFRs) and drive weak, but sustained outflows with mass-loading factors of similar to 0.2, transporting a substantial fraction (20%-60%) of the injected CR energy. These CR-driven outflows are launched not just from the galactic center, but across the entire disk, illustrating their pervasive dynamical influence. Galactic disks supported by CRs exhibit broader vertical structures compared to magnetic-field-dominated setups, although the scale heights are similar. CR feedback enhances magnetic flux transport to the circumgalactic medium (CGM), leading to a magnetically enriched CGM with field strengths of similar to 0.5 mu G, while reducing gas temperatures to less than or similar to 105 K. The CR energy is relatively smoothly distributed in the disk, with gradient lengths exceeding the typical size of molecular clouds, indicating that the CR behavior is not adiabatic.