Abstract Intense extreme-ultraviolet (XUV) pulses enable the investigation of XUV-induced non-linear processes and are a prerequisite for the development of attosecond pump - attosecond probe experiments. While highly non-linear processes in the XUV range have been studied at free-electron lasers (FELs), high-harmonic generation (HHG) has allowed the investigation of low-order non-linear processes. Here we suggest a concept to optimize the HHG intensity, which surprisingly requires a scaling of the experimental parameters that differs substantially from optimizing the HHG pulse energy. As a result, we are able to study highly non-linear processes in the XUV range using a driving laser with a modest (≈ 10 mJ) pulse energy. We demonstrate our approach by ionizing Ar atoms up to Ar^{5 +} , requiring the absorption of at least 10 XUV photons.