Aerodynamic interactions between two 30%-scale passenger vehicles in close proximity were examined experimentally in a large wind tunnel, with a focus on longitudinal separations up to two vehicle lengths, lateral separations up to one lane width, and combinations thereof. Part 1 of this paper described the longitudinal following (platooning) configurations of these results, while this paper concentrates on adjacent-lane influences and lateral-offset effects when platooning at a single separation distance. Test models were based on the DrivAer and Aero-SUV open-access geometries, each with slant-back (Notchback or Fastback) and square-back (Estateback) variants. This provided four distinct model pairings, not all of which were tested in each positional arrangement. Adjacent-lane results matched the trends from a smaller-scale study in a different wind tunnel using the same geometry pair, with small-but-distinct differences attributed to different blockage ratios in the two wind-tunnel studies. For three specific adjacent-lane arrangements, no significant differences were observed when changing the back variants of either of the models, suggesting that these proximity effects are primarily a function of model size, not shape. Four model pairs were tested with lateral offsets of 0.00, 0.25, 0.50 and 1.00 lane-widths, corresponding to approximately 0, 0.5, 1.0, and 2.0 model widths, at a longitudinal separation distance of 0.5 model lengths. The data suggest that, as crosswinds increase, peak drag reductions from platooning can be maintained by offsetting the vehicles laterally to maintain the follower model in the wake of the lead model, but the effect is sensitive to the shape of the lead vehicle. At 15° yaw angle, a quarter-lane offset (half-width offset) can maintain the system drag reduction at this separation distance.