We present new radial-velocity measurements of HAT-P-13 , a star with two previously known companions : a transiting giant planet “ b ” with an orbital period of 3 days , and a more massive object “ c ” on a 1.2 yr , highly eccentric orbit . For this system , dynamical considerations would lead to constraints on planet b ’ s interior structure , if it could be shown that the orbits are coplanar and apsidally locked . By modeling the Rossiter-McLaughlin effect , we show that planet b ’ s orbital angular momentum vector and the stellar spin vector are well-aligned on the sky ( \lambda = 1.9 \pm 8.6 deg ) . The refined orbital solution favors a slightly eccentric orbit for planet b ( e = 0.0133 \pm 0.0041 ) , although it is not clear whether it is apsidally locked with c ’ s orbit ( \Delta \omega = 36 _ { -36 } ^ { +27 } deg ) . We find a long-term trend in the star ’ s radial velocity and interpret it as evidence for an additional body “ d ” , which may be another planet or a low-mass star . Predictions are given for the next few inferior conjunctions of c , when transits may happen .