The problem of correlated electrons, as captured by the Hubbard model, is notorious for its analytical intractability. One promising approach involves the use of exactly solvable models, such as the Hatsugai-Kohmoto (HK) model. Recent work has demonstrated that the HK model is the minimal model that breaks the particle-hole symmetry of a Fermi liquid and falls within the same universality class as the Hubbard model [1]. This makes it an ideal framework for studying the universal properties of correlated systems, including correlated superconductors. This step was performed in [2] for an s-wave spin singlet pairing. We want to extend these findings to more complex pairing symmetries, including multiband superconductivity, in order to account for materials with more intricate electronic structures, such as metal-organic frameworks. [1] E. Huang et al. Nat. Phys. 18 5 511 (2022) [2] P. Phillips et al. Nat. Phys. 16 12 1175 (2020)