The incorporation of real-world data to supplement the analysis of trials and improve decision-making has spurred the development of statistical techniques to account for introduced confounding. Recently, "hybrid" methods have been developed through which measured confounding is first attenuated via propensity scores and unmeasured confounding is addressed through (Bayesian) dynamic borrowing. Most efforts to date have focused on augmenting control arms with historical controls. Here we consider augmenting treatment arms through "expanded access", which is a pathway of nontrial access to investigational medicine for patients with seriously debilitating or life-threatening illnesses. Motivated by a case study on expanded access, we developed a novel method (the ProPP) that provides a conceptually simple and easy-to-use combination of propensity score weighting and the modified power prior. Our weighting scheme is based on the estimation of the average treatment effect of the patients in the trial, with the constraint that external patients cannot receive higher weights than trial patients. The causal implications of the weighting scheme and propensity-score integrated approaches in general are discussed. In a simulation study, our method compares favorably with existing (hybrid) borrowing methods in terms of precision and type I error rate. We illustrate our method by jointly analyzing individual patient data from the trial and expanded access program for vemurafenib to treat metastatic melanoma. Our method provides a double safeguard against prior-data conflict and forms a straightforward addition to evidence synthesis methods of trial and real-world (expanded access) data.