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Even though tens of directly imaged companions have been discovered in the past decades, the number of directly confirmed multiplanet systems is still small. Dynamical analysis of these systems imposes important constraints on formation mechanisms of these wide-orbit companions. As part of the Young Suns Exoplanet Survey (YSES) we report the detection of a second planetary-mass companion around the 17 Myr-old, solar-type star TYC 8998-760-1 that is located in the Lower Centaurus Crux subgroup of the Scorpius-Centaurus association. The companion has a projected physical separation of 320 au and several individual photometric measurements from 1.1 to 3.8 microns constrain a companion mass of $6\pm1\,M_\mathrm{Jup}$, which is equivalent to a mass ratio of $q=0.57\pm0.10\%$ with respect to the primary. With the previously detected $14\pm3\,M_\mathrm{Jup}$ companion that is orbiting the primary at 160 au, TYC 8998-760-1 is the first directly imaged multiplanet system that is detected around a young, solar analog. We show that circular orbits are stable, but that mildly eccentric orbits for either/both components ($e > 0.1$) are chaotic on Gyr timescales, implying in-situ formation or a very specific ejection by an unseen third companion. Due to the wide separations of the companions TYC 8998-760-1 is an excellent system for spectroscopic and photometric follow-up with space-based observatories such as the James Webb Space Telescope.