We present the discovery of Kepler-129d (P_d_=7.2_-0.3_^+0.4^yr, m_sini_d__=8.3_-0.7_^+1.1^M_Jup_, e_d_=0.15_-0.05_^+0.07^) based on six years of radial-velocity observations from Keck/HIRES. Kepler-129 also hosts two transiting sub-Neptunes: Kepler-129b (P_b_= 15.79days, r_b_=2.40{+/-}0.04R{Earth}) and Kepler-129c (P_c_=82.20days, r_c_=2.52{+/-}0.07R{Earth}) for which we measure masses of m_b_~38{deg}, which could be torqued by Kepler-129 d if it is inclined by >~19{deg} relative to inner planets. Using N-body simulations, we provide additional constraints on the mutual inclination between Kepler-129d and inner planets by estimating the fraction of time during which two inner planets both transit. The probability that two planets both transit decreases as their misalignment with Kepler-129d increases. We also find a more massive Kepler-129c enables the two inner planets to become strongly coupled and more resistant to perturbations from Kepler-129d. The unusually high mass of Kepler-129c provides a valuable benchmark for both planetary dynamics and interior structure, since the best-fit mass is consistent with this 2.5R{Earth} planet having a rocky surface.