GJ 536 is a low-mass star, located 10 pc away from the Sun, that hosts a low-mass planet orbiting with a period of 8.71 days. Based on an analysis of the radial velocity (RV) time series obtained from the available data of the spectrographs HARPS, HARPS-N, CARMENES and HIRES, we announce the discovery of a second low-mass planet orbiting the star. We performed a RV global analysis on RV, spectroscopic activity indicators, and ASAS photometry, within the multidimensional Gaussian process framework, updated the parameters of GJ 536 b, and found significant evidence of the presence of a second planet. GJ 536 c is a low-mass planet (mp sin i = 5.89 ± 0.70 M⊕), orbiting with a period of 32.761 ± 0.015 days, at a distance of 0.1617 ± 0.0028 au from its parent star. It induces an RV semi-amplitude of 1.80 ± 0.20 m s‑1. Given its distance to the star, it receives a flux of 1.692 ± 0.069 F⊕, for an equilibrium temperature of 290.5 ± 9.5 K. We update the mass of the planet GJ 536 b to mp sin i = 6.37 ± 0.38 M⊕. The orbits of both planets are consistent with circular. We explored the use of statistical Doppler imaging on the photometric and RV data, and find a tentative projected obliquity of the stellar rotation axis of 58‑19+16 deg. Current evidence does not support the presence of additional planets with masses >5 M⊕ for orbital periods up to 100 days, or >10 M⊕ for periods up to 1000 days.