In on-line social networks, innovations in the presence of one or more influences disseminate through the topological structure of the networks rapidly. In reality, various influences normally coexist in the same context and have subtle relations, such as supportive, contradictory and competitive relations, affecting the users' decisions of adopting any innovations. Therefore, modelling diffusion process of multiple influences is an important, yet challenging research question. By employing the agent-based modelling, in this paper, a distributed approach has been proposed to model the diffusion process of multiple influences in social networks. The proposed model has been applied in the undesirable influence minimisation problem, where the time series is taken into consideration. The experimental results show our model can be utilised to minimise the adverse impact of a certain influence by injecting other influences. Furthermore, the proposed model also sheds light on understanding, investigating and analysing multiple influences in social networks.