Refinement of Bayesian network (BN) structures using new data becomes more and more relevant. Some work has been done there; however, one problem has not been considered yet – what to do when new data have fewer or more attributes than the existing model. In both cases, data contain important knowledge and every effort must be made in order to extract it. In this paper, we propose a general merging algorithm to deal with situations when new data have different set of attributes. The merging algorithm updates sufficient statistics when new data are received. It expands the flexibility of BN structure refinement methods. The new algorithm is evaluated in extensive experiments and its applications are discussed at length.