We present a new mechanical model and numerical method for simulating a whole family of shear-rigid shells, i.e., Kirchhoff–Love shells, within some bulk domain, in a single computation. The approach builds upon previous work on the simultaneous analysis of multiple membranes [3] or Reissner–Mindlin shells [4]. However, additional challenges arise for Kirchhoff–Love shells due to the increased continuity requirements of the mechanical model. The shells are continuously distributed in a three-dimensional bulk domain, with their geometries described implicitly via a level-set function. The framework of the tangential differential calculus [1, 2] is used for defining geometric quantities and differential operators. This permits a coordinate-free formulation, being perfectly suited for implicit geometry descriptions. The increased inter-elemental continuity requirements of Kirchhoff–Love shells are addressed by a mixed-hybrid approach based on the Hellinger–Reissner principle. In addition to the displacements, the components of the moment tensor are introduced as primary unknowns, lowering the continuity requirements from C1 to C0. As this approach increases the number of degrees of freedom, a hybridization scheme as outlined in [5] is applied. By weakly reinforcing the continuity requirements of the moments across elements with a Lagrange multiplier, the components of the moment tensor may be eliminated locally, leading to a computationally efficient formulation. The accuracy and higher-order convergence of the method are confirmed by multiple numerical tests.