Strongly interacting electrons in clean two-dimensional devices are theorized to exhibit many distinct transport regimes, such as ballistic, hydrodynamic, or diffusive. Realistic samples often lie in crossover regimes between these idealized limits. We show how a single experiment on a multiterminal device can distinguish these regimes and constrain the relevant scattering rates without space-resolved imaging. Using a linearized Boltzmann model in a five-terminal geometry, we find that current partition among the drain contacts diagnoses the ballistic-hydrodynamic-Ohmic crossover and allows extraction of momentum-relaxing and momentum-conserving scattering rates in the crossover regime. The same geometry also exhibits clear signatures of the tomographic regime, potentially allowing for a quantitative discrimination between viscous and tomographic flow in experiments. Our results demonstrate that multiterminal devices are a simpler experimental route to characterize transport regimes in electron liquids, relative to space-resolved imaging experiments.