Spontaneous symmetry breaking in interacting fermionic systems leads to a proliferation of independent scattering channels, making the treatment of many-body effects particularly challenging. In this talk, I present two complementary studies addressing the interplay between magnetism, strong correlations, and emergent spectral features in broken symmetry phases of the Hubbard model. First, I introduce an extension of the Two-Particle-Self-Consistent approach (TPSC) to efficiently describe SU(2)-broken magnetic phases. Applied to the antiferromagnetic phase of the Hubbard model, this framework enforces sum rules while preserving Goldstone modes and incorporating vertex corrections. These corrections play a crucial role in renormalizing the Higgs resonance, which we identify as a well-defined excitation in the spin-longitudinal susceptibility. Next, I turn to a variant of the Hubbard model that hosts altermagnetic states—magnetic phases that exhibit Dirac-like band structures. Using a combination of Hartree-Fock and Dynamical Mean Field Theory (DMFT), we show that interaction effects can induce unexpected spectral features, including the re-emergence of Dirac points at high energies near Mott insulating regimes. Additionally, we explore how perturbations can drive topological phase transitions, offering a route to engineer non-trivial electronic states.