Intense extreme-ultraviolet (XUV) pulses enable the investigation of XUV-induced nonlinear processes and are a prerequisite for the development of attosecond pump -attosecond probe experiments. While highly nonlinear processes in the XUV range have been studied at free-electron lasers (FELs), high-harmonic generation (HHG) has allowed the investigation of low-order nonlinear 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 nonlinear 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.Three key features of intense XUV pulses from FEL and HHG sources have opened up new possibilities for a range of fields from life science to material science and fundamental physics: (i) Intense XUV pulses provide the possibility to perform pump-probe experiments, in which a first XUV pump pulse initiates dynamics in an atom or a molecule, and these dynamics are probed by a second, time-delayed XUV probe pulse. This capability has been extensively used with femtosecond time resolution at FELs (see e.g. Ref.[1]) and has been implemented with attosecond time resolution using HHG sources [2, 3]. (ii) Intense, coherent XUV pulses have enabled singleshot coherent diffractive imaging (CDI) of isolated nanotargets with a resolution in the tens of nanometers range. While these experiments are predominantly performed at FELs [4], CDI on He nanodroplets using an intense HHG source was recently reported [5]. (iii) High XUV intensities enable the study of nonlinear optics in this spectral range. Examples include multiple ionization of atoms [6] and XUV-driven four-wave mixing schemes [7].Advantages of HHG sources compared to FELs include their smaller size and lower costs resulting in easier access to these sources. Another important point is that two-color XUV-optical pump-probe experiments, which are one of the preferred applications of ultrashort XUV pulses, are challenging at FELs due to timing jitter between the optical and XUV beams [8]. Such experiments are routinely performed using HHG sources, with a time resolution extending into the attosecond domain, given the fact that attosecond pulses based on HHG have been generated for more than 10 years [9].The most common scheme used to generate intense HHG pulses requires powerful near-infrared (NIR) pulses that are loosely focused into a gas medium to increase the generation volume [3, 10-13]. It has been shown that the HHG pulse energy increases with increasing NIR focal length [14]. In contrast, we demonstrate in this paper that for a given laboratory size the XUV intensity on target can be optimized by using an NIR focusing element with a relatively short focal length. This enables the 5 10 15 d in m 5 10 15 dNIR in m 1 2 3 4 XUV beam waist radius ( ...