Several approaches to power scaling of mode-locked thin-disk oscillators exist. One of these approaches is based on the increased gain provided by multiple passes through the thin-disk laser medium. For the first time, to the best of our knowledge, we applied this approach to a Kerr-lens mode-locked thin-disk oscillator. The so obtained additional gain allowed mode-locked operation with up to 50% output coupling rate. This first demonstration is of particular importance for gain media with inherently low-emission cross sections and paves the way to even more powerful Kerr-lens mode-locked thin-disk oscillators. Moreover, the experimental results indicate an increased self-amplitude modulation related to an overall increase in the soft-aperture Kerr-lens effect.