Since its first demonstration in 2016, the multi-pass spectral broadening technique has covered impressive ranges of pulse energy (3 µJ - 100 mJ) and peak power (4 MW - 100 GW). Energy scaling of this technique into the joule-level is currently limited by phenomena such as optical damage, gas ionization and spatio-spectral beam inhomogeneity. These limitations can be overcome by the novel multi-pass convex-concave arrangement, which exhibits crucial properties such as large mode size and compactness. In a proof-of-principle experiment, 260 fs, 15 µJ and 200 µJ pulses are broadened and subsequently compressed to approximately 50 fs with 90% efficiency and excellent spatio-spectral homogeneity across the beam profile. We simulate the proposed concept for spectral broadening of 40 mJ and 1.3 ps input pulses and discuss the possibility of further scaling.