Large-scale computational fluid dynamics (CFD) applications often rely on distributed-memory parallel solvers that partition the computational domain into communicating subdomains. Numerical methods, particularly preconditioners, must incorporate domain decomposition strategies tailored to this setup, typically employing either partitioned or monolithic coupling approaches. While domain decomposition (DD) strategies might initially seem counterintuitive in the context of reduced-order models (ROMs) for parametric partial differential equations (PDEs)—since they can increase the reduced dimensions of the linear systems—they can be advantageous in specific scenarios. In particular, for multi-physics and multi-scale problems, DD-ROMs naturally enhance ROM accuracy by isolating and addressing parameter-dependent behavior within distinct regions of the domain. This approach can mitigate accuracy losses when approximating solutions for unseen parameters. Moreover, DD-ROMs with non-uniform reduced dimensions share similarities with hp-discretizations, optimizing resource allocation by tailoring the resolution to localized requirements. We propose novel domain repartitioning strategies that redefine domain decompositions compared to the full-order model (FOM), minimizing quantities of interest such as local Kolmogorov n-widths. The coupling conditions at the reduced-order level are efficiently enforced using discontinuous Galerkin (DG) method penalties. We demonstrate the effectiveness of these strategies on Friedrichs' systems and multi-physics problems, with applications drawn from biomedical contexts.