An extension of a set of marginals (small-dimensional distributions) is a joint probability distribution that is a ”good” representative of the knowledge (about the problem area) contained in the marginals. ”Good” means with respect to the subsequent decision-making for which the extension is needed. In the context of probabilistic expert systems, constructing the extension from the marginals may be referred to as the knowledge integration [4], reconstructability analysis [9] or marginal problem. The paper surveys different types of known extensions and on the basis of underlying principles and considerations, new types of extensions — the EEV-centroid and the weighted centroid are suggested.