Widening a highway toll plaza, border crossing or other checkpoint by adding travel lanes and vehicle-processing stations in parallel fashion can be expensive, and sometimes even infeasible. Rather than expanding laterally, checkpoint capacities can be increased by branching or staggering the vehicle-processing stations, or by placing them in tandem. Analytical models are formulated to estimate the vehicle-processing capacities achievable via these layouts. The models indicate that tandem designs tend to produce the highest capacities among the three alternatives. Other insights are unveiled as well.