Recently, the assisted bidirectional Glenn (ABG) procedure has been proposed as an alternative to the modified Blalock–Taussig shunt (mBTS) operation for neonates with single-ventricle physiology. Despite success in reducing heart workload and maintaining sufficient pulmonary flow, the ABG also raised the superior vena cava (SVC) pressure to a level that may not be tolerated by infants. To lower the SVC pressure, we propose a modified version of the ABG (mABG), in which a shunt with a slit-shaped nozzle exit is inserted at the junction of the right and left brachiocephalic veins. The proposed operation is compared against the ABG, the mBTS, and the bidirectional Glenn (BDG) operations using closed-loop multiscale simulations. Both normal (2.3 Wood units-m2) and high (7 Wood units-) pulmonary vascular resistance (PVR) values are simulated. The mABG provides the highest oxygen saturation, oxygen delivery, and pulmonary flow rate in comparison to the BDG and the ABG. At normal PVR, the SVC pressure is significantly reduced below that of the ABG and the BDG (mABG: 4; ABG: 8; BDG: 6; mBTS: 3 mmHg). However, the SVC pressure remains high at high PVR (mABG: 15; ABG: 16; BDG: 12; mBTS: 3 mmHg), motivating an optimization study to improve the ABG hemodynamics efficiency for a broader range of conditions in the future. Overall, the mABG preserves all advantages of the original ABG procedure while reducing the SVC pressure at normal PVR.