We combine theory, numerical simulation, and experiments to investigate the breakup of two identical droplets entering a Y-junction with controlled spatial offset by which the second droplet trails the first. Based on fully resolved 3D simulations, we describe the flow physics leading to breakup. Scaling arguments, numerical simulation, and experiments consistently show that for small initial offset, breakup always occurs with the droplet fragment volume depending linearly on the offset. Above a critical offset, which increases with the capillary number, the droplets enter the constriction sequentially without breakup. Our results are relevant for understanding the breakup behavior in a dense emulsion flowing through a linearly converging channel leading to a constriction. Such geometry is commonly used for the serial interrogation of droplet content in droplet microfluidic applications, where droplet breakup can limit the maximum throughput for such process. For capillary numbers up to Ca similar or equal to 10(-2), the results from the two-droplet system in a Y-junction are consistent with breakup observations in dense emulsions flowing through a linearly converging channel. The deterministic relation between initial offset and resulting breakup in the two-droplet system suggests that the stochasticity that is observed in the breakup of a dense emulsion arises from multidroplet interactions. The numerical value of the prefactor in the linear relation between initial offset and droplet fragment volume determined from experiments differs slightly from the one extracted from fully resolved numerical simulations. This discrepancy suggests that even at very high bulk surfactant concentrations, the rate-limiting surfactant adsorption kinetics allows for Marangoni stresses to develop and modify the droplet dynamics.