Therapies utilizing autologous mesenchymal cell delivery are being investigated as anti-inflammatory and regenerative treatments for a broad spectrum of age-related diseases, as well as various chronic and acute pathological conditions. Easily available allogeneic full-term human placenta mesenchymal stromal cells (pMSCs) were used as a potential pro-regenerative, cell-based therapy in degenerative diseases, which could be applied also to elderly individuals. To explore the potential of allogeneic pMSCs transplantation for pro-regenerative applications, such cells were isolated from five different term-placentas, obtained from the dissected maternal, endometrial (mpMSCs), and fetal chorion tissues (fpMSCs), respectively. The proliferation rate of the cells in the culture, as well as their shape, in vitro differentiation potential, and the expression of mesenchymal lineage and stem cell markers, were investigated. Moreover, we studied the expression of immune checkpoint antigen CD276 as a possible modulation of the rejection of transplanted non-HLA-matched homologous or even xeno-transplanted pMSCs. The expression of the cell surface markers was also explored in parallel in the cryosections of the relevant intact placenta tissue samples. The expansion of pMSCs in a clinical-grade medium complemented with 5% human platelet lysate and 5% human serum induced a significant expression of CD276 when compared to mpMSCs expanded in a commercial medium. We suggest that the expansion of mpMSCs, especially in a medium containing platelet lysate, elevated the expression of the immune-regulatory cell surface marker CD276. This may contribute to the immune tolerance towards allogeneic pMSC transplantations in clinical situations and even in xenogenic animal models of human diseases. The endurance of the injected comparably young human-term pMSCs may promote prolonged effects in clinical applications employing non-HLA-matched allogeneic cell therapy for various degenerative disorders, especially in aged adults.