A numerical procedure is presented for the scaling of lean aeronautical gas turbine combustors to different thrust classes. The procedure considers multiple operating points and aims for a self-similar flow field with respect to a reference configuration. The developed scaling approach relies on an optimization-based workflow which involves automated geometry and grid generation, unsteady Reynolds-averaged Navier-Stokes (URANS) simulations and post-processing. Kriging is applied as a meta model to identify new sets of geometrical parameters. A scaling function based on pressure loss, axial location of heat release, pilot air split and the temperature profile at the combustor exit is proposed. A generic internally-staged lean-burn high pressure aeronautical combustor has been designed to serve as a first verification test case with reactive flow characteristics comparable to real combustion chambers. The burner geometry is parameterized by 23 free parameters which are altered within the scaling process. The developed procedure is applied to scale the combustor to a lower thrust class considering multiple operating points simultaneously: take-off, approach and idle. In total, 65 different combustor variants have been evaluated within the scaling procedure. The final combustor configuration, scaled to a lower thrust class, shows good agreement to the reference configuration in terms of the scaling targets and reasonably resembles the emission indices. Integrating the scaling procedure into the design process of future combustion systems could reduce the required design iterations and thereby contribute to significantly reduced development times and costs.