Context. Open cluster (OC) stars share the same age and metallicity, and, in general, their age and mass can be estimated with higher precision than for field stars. For this reason, OCs are considered an importantlaboratory to study the relation between the physical properties of the planets and those of their host stars, and the evolution of planetary systems. However, only a handful of planets have been discovered around OC main-sequence stars so far, all of them in single-planet systems. For this reason we started an observational campaign within the GAPS collaboration to search for and characterize planets in OCs Aims: We monitored the Praesepe member Pr 0211 to improve our knowledge of the eccentricity of the hot Jupiter (HJ) that is already known to orbit this star and search for additional intermediate-mass planets. An eccentric orbit for the HJ would support a planet-planet scattering process rather than a disk-driven migration after its formation. Methods: From 2012 to 2015, we collected 70 radial velocity (RV) measurements with HARPS-N and 36 with TRES of Pr 0211. Simultaneous photometric observations were carried out with the robotic STELLA telescope to characterize the stellar activity. We discovered a long-term trend in the RV residuals that we show as being due to the presence of a second, massive, outer planet. Orbital parameters for the two planets are derived by simultaneously fitting RVs and photometric light curves, with the activity signal modelled as a series of sinusoids at the rotational period of the star and its harmonics. Results: We confirm that Pr 0211b has a nearly circular orbit (e = 0.02 ± 0.01), with an improvement of a factor two with respect to the previous determination of its eccentricity, and estimate that Pr 0211c has a mass Mp sin i = 7.9 ± 0.2 MJ, a period P> 3500 days and a very eccentric orbit (e> 0.60). This kind of peculiar system may be typical of open clusters if the planet-planet scattering phase, which lead to the formation of HJs, is caused by stellar encounters rather than by unstable primordial orbits. Pr 0211 is the first multi-planet system discovered around an OC star. Based on data obtained with (i) the HARPS-N spectrograph on the Italian Telescopio Nazionale Galileo (TNG), operated on the island of La Palma by the INAF - Fundacion Galileo Galilei (Spanish Observatory of Roque de los Muchachos of the IAC); (ii) the Tillinghast Reflector Echelle Spectrograph (TRES) on the 1.5-m Tillinghast telescope, located at the Smithsonian Astrophysical Observatory's Fred L. Whipple Observatory on Mt. Hopkins in Arizona; (iii) the STELLA robotic telescopes in Tenerife, an AIP facility jointly operated by AIP and IAC. Full Tables 1, 3-5 are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/588/A118