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Based on recently-taken and archival HARPS, FEROS and HIRES radial velocities (RVs), we present evidence for a new planet orbiting the first ascent red giant star HD33142 (with an improved mass estimate of 1.52$\pm$0.03 M$_\odot$), already known to host two planets. We confirm the Jovian mass planets HD33142 b and c with periods of $P_{\rm b}$ = 330.0$_{-0.4}^{+0.4}$ d and $P_{\rm c}$ = 810.2$_{-4.2}^{+3.8}$ d and minimum dynamical masses of $m_{\rm b}\sin{i}$ = 1.26$_{-0.05}^{+0.05}$ M$_{\rm Jup}$ and $m_{\rm c}\sin{i}$ = 0.89$_{-0.05}^{+0.06}$ M$_{\rm Jup}$. Furthermore, our periodogram analysis of the precise RVs shows strong evidence for a short-period Doppler signal in the residuals of a two-planet Keplerian fit, which we interpret as a third, Saturn-mass planet with $m_\mathrm{d}\sin{i}$ = 0.20$_{-0.03}^{+0.02}$ M$_{\rm Jup}$ on a close-in orbit with an orbital period of $P_{\rm d}$ =89.9$_{-0.1}^{+0.1}$ d. We study the dynamical behavior of the three-planet system configurations with an N-body integration scheme, finding it long-term stable with the planets alternating between low and moderate eccentricities episodes. We also performed N-body simulations, including stellar evolution and second-order dynamical effects such as planet-stellar tides and stellar mass-loss on the way to the white dwarf phase. We find that planets HD33142 b, c and d are likely to be engulfed near the tip of the red giant branch phase due to tidal migration. These results make the HD33142 system an essential benchmark for the planet population statistics of the multiple-planet systems found around evolved stars.