  Aims. For more than 1.5 years we monitored spectroscopically the star KELT-6
(BD+312447), known to host the transiting hot Saturn KELT-6b, because a
previously observed long-term trend in radial velocity time series suggested
the existence of an outer companion. Methods. We collected a total of 93 new
spectra with the HARPS-N and TRES spectrographs. A spectroscopic transit of
KELT-6b 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$_{\rm p}$sini=3.71$\pm$0.21 M$_{\rm Jup}$ and a
moderately eccentric orbit ($e=0.21_{-0.036}^{+0.039}$) of period P$\sim$3.5
years. We improved the orbital solution of KELT-6b 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 $\lambda$=$-$36$\pm$11 degrees. We improved the KELT-6b
transit ephemeris from photometry, and we provided new measurements of the
stellar parameters. KELT-6 appears as an interesting case to study the
formation and evolution of multi-planet systems.
