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Plasmasphere refilling is modeled using an upgraded version of the Naval Research Laboratory SAMI2 (Sami2 is Another Model of the Ionosphere) ionosphere/plasmasphere code. In this implementation of SAMI2, two fluid species are used for H+, each having a source in only one magnetic hemisphere. This is the first comprehensive plasmasphere model with two-stream H+. With two counterstreaming H+ fluids, artificial shocks or compressions at high altitude are avoided during storms and early-stage refilling. For late-stage refilling, runs with two-stream SAMI2 validate previous SAMI2 (one H+ fluid) refilling rates. At ionospheric altitudes (less than or similar to 2,000 km), where the single-fluid approximation is valid for each ion, two-stream SAMI2 results agree closely with SAMI2 results.