Accurate and continuous flow data are crucial for effective water management in large river basins worldwide. However, these catchments often face challenges regarding data continuity in the mainstream and their tributaries. This study proposes a methodological framework for enhancing flow data continuity that uses a staged calibration scheme of Soil and Water Assessment Tool (SWAT) modeling with an appropriate satellite precipitation product (SPP) for each watershed. This framework is successfully applied in the Mun-Chi River Basin, the largest tributary of the Lower Mekong River, over a 20-year period at 34 stations. The staged calibration involves partitioning the catchment into smaller sub-catchments, guided by the flow monitoring stations and flow discontinuity structures such as dams. The sequential calibration from upstream to downstream partitions the overall model calibration challenge into smaller problems and contributes to a more efficient and accurate calibration and validation. Alternative SPPs were considered to overcome monitoring gaps. Their bias was corrected using quantile mapping, and their performance was evaluated with flow simulations using the SWAT model. The assessment indicates that the CMORPH-CRT product, with a spatial resolution of 0.25°, demonstrates good suitability for hydrological modeling of the Mun-Chi River Basin. The proposed methodological framework provides a continuous time series of flow discharge at multiple stations within the watershed, offering valuable insights for sustainable water resource management strategies in river systems under changing climate and land use conditions, and supporting future studies on environmental issues.