Consensus reaching processes are applied in group decision making problems to reach a mutual agreement among a group of decision makers before making a common decision. Different consensus models have been developed to facilitate consensus reaching processes. However, new trends bring diverse challenges in group decision making, such as the modelling of different types of information and of large groups of decision makers, together with their attitude to achieve agreements. These challenges require the capacity to deal with heterogenous frameworks, and the automation of consensus reaching processes by means of consensus support systems. In this paper, we propose a consensus model in which decision makers can express their opinions by using different types of information, capable of dealing with large groups of decision makers. The model incorporates the management of the group’s attitude towards consensus by means of an extension of OWA aggregation operators aimed to optimize the overall consensus process. Eventually, a novel Web-based consensus support system that automates the proposed consensus model is presented