The rotating search coil is a precise and widely used tool for measuring the magnetic field harmonics of accelerator magnets. This paper deals with combining several such multipole measurements, in order to cover magnet apertures largely exceeding the diameter of the available search coil.The method relies on the scaling laws for multipole coefficients and on the method of analytic continuation along zero-homotopic paths. By acquiring several measurements of the integrated magnetic flux density at different transverse positions within the bore of the accelerator magnet, the uncertainty on the field harmonics can be reduced at the expense of tight tolerances on the positioning. These positioning tolerances can be kept under control by mounting the rotating coil and its motor-drive unit on precision alignment stages. Therefore, the proposed technique is able to yield even more precise results for the higher-order field components than a dedicated rotating search coil of larger diameter. Moreover, the versatility of the measurement bench is enhanced by avoiding the construction of rotating search coils of different measurement radii.