Unlike many complex networks studied in the literature, social networks rarely exhibit regular cooperative behavior such as synchronization (referred usually as consensus or agreement of the opinions). This requires a development of mathematical models that capture the complex behavior of real social groups, where opinions and the actions related to them form clusters of different size, and yet are sufficiently simple to be examined. One such model, proposed in [1], deals with scalar opinions and extends the idea in [2] of iterative pooling in a way to take into account the actors’ prejudices, caused by some exogenous factors and leading to disagreement in the final opinions. In this paper, we offer two extensions, where opinions are multidimensional, representing the agents’ attitudes on several topics, and those topic-specific attitudes are interrelated. We examine convergence of the proposed model and find explicitly the steady opinions of the agents. Although our model assumes synchronous communication among the agents, we show that the same final opinion may be achieved “on average” via asynchronous randomized gossip-based protocol.