We study the band structure and topology of magnons for a Heisenberg model with Dzyaloshinskii–Moriya (DM) interaction on a deformed Kagome lattice. For simplicity, we focus on a periodically deformed lattice with hexagonal symmetry and an enlarged unit cell. This enlarged unit cell gives rise to a more complex band structure than in the undeformed case. Analyzing band topology, there is a distinction between the topologically trivial case with anti-ferromagnetic coupling and the topologically non-trivial case with ferromagnetic coupling. In the anti-ferromagnetic case, a spin-space symmetry, also present in the classical ground state, enforces these topologically trivial states. In the ferromagnetic case, this symmetry is spontaneously broken by the classical ground state. Consequently, the band structure also hosts numerous topological features. Specifically, we observe many topological transitions and bands with Chern numbers ranging from $+2$ to $-2$, which makes the system richer than in the undeformed case. This emergent topological structure demonstrates that deformed magnets can host new and exciting physics.