The GPS1 catalog was released in 2017. It delivered precise proper motions for around 350 million sources across three-fourths of the sky down to a magnitude of $rsim20$,mag. In this study, we present GPS1+ the extension GPS1 catalog down to $rsim22.5$,mag, based on {it Gaia} DR2, PS1, SDSS and 2MASS astrometry. The GPS1+ totally provides proper motions for $sim$400 million sources with a characteristic systematic error of less than 0.1masyr. This catalog is divided into two sub-samples, i.e., the primary and secondary parts. The primary $sim$264 million sources have either or both of the {it Gaia} and SDSS astrometry, with a typical precision of 2.0-5.0 masyr. In this part, $sim$160 million sources have {it Gaia} proper motions, we provide another new proper motion for each of them by building a Bayesian model. Relative to {it Gaia}s values, the precision is improved by $sim$0.1,dex on average at the faint end; $sim$50 million sources are the objects whose proper motions are missing in {it Gaia} DR2, we provide their proper motion with a precision of $sim$4.5masyr; the remaining $sim$54 million faint sources are beyond {it Gaia} detecting capability, we provide their proper motions for the first time with a precision of 7.0 masyr. However, the secondary $sim$136 million sources only have PS1 astrometry, the average precision is worse than 15.0 masyr. All the proper motions have been validated using QSOs and the existing {it Gaia} proper motions. The catalog will be released on-line and available via the VO-TAP Service, or via the National Astronomical Data Center serviced by China-VO: https://nadc.china-vo.org/data/data/gps1p/f.
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