The open position service of Global Navigation Satellite System (GNSS), namely single point positioning (SPP), has been widely used in vehicle navigation and environmental monitoring, etc, owing to its simple algorithm and low cost. Since multi-system integration can significantly improve SPP performance and the four GNSSs, namely BDS (BDS-3/BDS-2), GPS, GLONASS and Galileo, have recently been almost fully deployed, it is necessary to assess the four-system integrated SPP (FISPP) performance under the current constellation status. In this study, we first evaluate the current situations of the four constellations from three aspects: availability, code multipath and noise (CMN), and the accuracy of broadcast ephemeris. Subsequently, the datasets from 141 Multi-GNSS Experiment (MGEX) stations on October 25 to 31, 2020, are used to assess the performance of FISPP under open sky and occlusion environments. The positioning accuracy of FISPP is 0.484/0.987/2.084, 0.525/0.897/2.340, and 1.932/2.671/8.502 m in the east/north/up directions at a global service rate of 100.0%, 99.8%, and 69.4% under a cut-off elevation angle of 10°, 30°, and 50°, respectively. For comparison, the positioning results of the other seven system combination cases (GPS-only, GLONASS-only, Galileo-only, BDS-only, GPS/GLONASS, GPS/Galileo, and GPS/BDS SPP) are also provided. The code observation residuals are also presented for comprehensive analysis. In addition, the performance of smartphone-based FISPP is also assessed.