In this study, we develop a Multi-constellation Global Navigation Satellite System (GNSS) Receiver Differential Code Bias (MGR-DCB) model. The model estimates the receiver DCBs for the Global Positioning System (GPS), BeiDou and Galileo signals from the ionosphere-corrected geometry-free linear combinations of the code observations. In order to account for the ionospheric delay, a Regional Ionospheric Model (RIM) over Europe is developed. GPS observations from 60 International GNSS Servoce (IGS) and EUREF reference stations are processed in the Bernese-52 Precise Point Positioning (PPP) module to estimate the Vertical Total Electron Content (VTEC). The RIM has spatial and temporal resolutions of 1 degrees x 1 degrees and 15 minutes, respectively. The receiver DCBs for three stations from the International GNSS Service Multi-GNSS Experiment (IGS-MGEX) are estimated for three different days. The estimated DCBs are compared with the MGEX published values. The results show agreement with the MGEX values with mean difference and Root Mean Square Error (RMSE) values less than 1 ns. In addition, the combined GPS, BeiDou and Galileo VTEC values are evaluated and compared with the IGS Global Ionospheric Maps (IGS-GIM) counterparts. The results show agreement with the GIM values with mean difference and RMSE values less than 1 Total Electron Content Unit (TECU).