Procurement decisions play a vital part in the sustainable transformation of the supply chain. Till now, a variety of supplier selection and lot-sizing models have been suggested, in particular, focusing on carbon emissions in a deterministic environment. It is noted that stressing only on carbon emissions cannot fully transform a sustainable supply chain. The present study argues that with carbon footprint, other dimensions, such as social sustainability, water footprint, recycled material use, solid and liquid waste, need to be considered in sustainable procurement decisions. To fill the gaps, this study proposed a three-stage multi-objective multi-supplier, multi-period joint supplier selection, and a lot-sizing model, taking into account carbon footprint, water footprint, solid and liquid waste, and use of recycled materials in a stochastic environment. The model optimizes three objectives (cost, carbon emission, and social sustainability). The model considers different model parameters as uncertain, such as costs, emission, solid waste, liquid waste, recycled material, quality rejection, and capacity. The present study suggests how to quantify social sustainability and further use it in the lot-sizing model. The proposed study has been carried out in three stages. In the first stage, BWM (Best-Worst method) and TOPSIS are applied to evaluate suppliers' social scores. In the second stage, the suppliers' social scores are used in the proposed possibilistic lot-sizing model. In the third stage, various trade-off curves are generated by applying the ε-constraint method. The model produces distinct optimal solutions for different uncertainty levels, which are used to create trade-off curves among the cost, emission, and social dimensions. The results facilitate decision-makers to decide the lot-size in an ambiguous environment.