Over the past years, the International GNSS Service (IGS) has been putting efforts into extending its service by setting up and running the Multi-GNSS experiment and pilot project (MGEX). Several MGEX analysis centers (ACs) contribute by providing solutions containing not only GPS and GLONASS but also Galileo, BeiDou, and QZSS. As the current IGS combination software can only handle the orbits of one constellation at a time, it requires substantial modifications to obtain a consistent MGEX orbit product. In this contribution, we present a least-squares framework for a Multi-GNSS orbit combination, where the weights used to combine the ACs’ orbits are determined by least-squares variance component estimation. We introduce and compare two weighting strategies, where either AC-specific weights or AC and constellation-specific weights are used. An automated Z-score test is implemented yielding a common set of core satellites that are used to determine the weights. Both strategies are tested using MGEX orbit solutions for a period of two and a half years. They yield similar results with an agreement with the ACs’ orbits at the one centimeter level for GPS and up to a few centimeters for the other constellations. The 3D-RMS is generally slightly better with the AC and constellation weighting. A comparison of our combination approach with the official IGS combination using three years of GPS and GLONASS orbits shows an agreement of better than 5 mm and 12 mm for GPS and GLONASS, respectively, while the agreement of the official IGS combination with the ACs’ GPS solutions is only around 15mm. An external validation using satellite laser ranging shows that the mean residuals of our combined products are around −3mm for Galileo, 6mm for GLONASS, −8mm for BeiDou, and −31mm for QZSS.