Global Software Development (GSD) projects comprise several critical cost drivers that affect the overall project cost and budget overhead. Thus, there is a need to amplify the existing model in GSD context to reduce the risks associated with cost overhead. Motivated by this, the current work aims at amplifying the existing algorithmic model with GSD cost drivers to get efficient estimates in the context of GSD. To achieve the targeted research objective, current state-of-the-art cost estimation techniques and GSD models are reported. Furthermore, the current study has proposed a conceptual framework to amplify the algorithmic COCOMO-II model in the GSD domain to accommodate additional cost drivers empirically validated by a systematic review and industrial practitioners. The main phases of amplification include identifying cost drivers, categorizing cost drivers, forming metrics, assignment of values, and finally altering the base model equation. Moreover, the proposed conceptual model's effectiveness is validated through expert judgment, case studies, and Magnitude of Relative Estimates (MRE). The obtained estimates are efficient, quantified, and cover additional GSD aspects than the existing models; hence we could overcome the GSD project's overall risk by implementing the model. Finally, the results indicate that the model needs further calibration and validation.