Aims. For more than 1.5 years we spectroscopically monitored the star KELT-6 (BD+31 2447), which is known to host the transiting hot-Saturn KELT-6 b, because a previously observed long-term trend in radial velocity time series suggested that there is an outer companion. Methods. We collected a total of 93 new spectra with the HARPS-N and TRES spectrographs. A spectroscopic transit of KELT-6 b was observed with HARPS-N, and simultaneous photometry was obtained with the IAC-80 telescope. Results. We proved the existence of an outer planet with a mininum mass M(p)sin i = 3.71 +/- 0.21 M-Jup and a moderately eccentric orbit (e = 0.21(-0.036)(+0.039)) of period P similar to 3.5 years. We improved the orbital solution of KELT-6 b and obtained the first measurement of the Rossiter-McLaughlin effect, showing that the planet has a likely circular, prograde, and slightly misaligned orbit with a projected spin-orbit angle of lambda = - 36 +/- 11 degrees. We improved the KELT-6 b transit ephemeris from photometry and provide new measurements of the stellar parameters. KELT-6 appears as an interesting case for studying the formation and evolution of multi-planet systems.