We investigate multicomponent superconductivity in twisted bilayer cuprates with order parameter s+d₁ e^(iφ₁)+d₂ e^(iφ₂), where s=s₁+s₂ is the layer-symmetric s-wave pairing and dᵢ is the d-wave pairing in layer i. When φ₁-φ₂≠ 0,π, this three-component state spontaneously breaks time-reversal and C₄ rotational symmetries and can realize a topologically nontrivial phase. Ginzburg-Landau analysis and self-consistent mean-field calculations show that this state is stabilized over a broad parameter regime. We further identify nematic Kerr anisotropy as a key signature distinguishing it from s+id and d₁+e^(iφ)d₂, and find that its Josephson critical current remains sizable near the 45^∘ twist. Our results show that s-wave pairing does not preclude chiral topological superconductivity, pointing to twisted cuprates as a more robust platform than previously appreciated.