We present a novel framework for topological shape optimization of curved non-conforming multi-patch and trimmed thick-shells subjected to external loads. Our method integrates the level set method (LSM) with a diffuse interface, a Hadamard shape derivative, and multi- patch isogeometric analysis (IGA) into a gradient descent algorithm to systematically capture the evolution of the shape. This integration enables us to directly manipulate CAD-compatible geometries and analysis techniques and to obtain the results as a CAD surface. The novelty lies in the utilization of multi-patch IGA models based on NURBS functions, which allows us to simultaneously maximize the stiffness and minimize the volume of the shell by searching for an optimal material distribution within its middle surface. The material is modeled under a small strain assumption in linear elasticity using a Reissner–Mindlin kinematic shell model in plane stress. The effectiveness of our approach is demonstrated on several curved conforming and non-conforming multi-patch geometries in 3D.