Abstract Knowledge spaces are structures for the efficient assessment of the knowledge state of a student in a given field of knowledge. Existing procedures for constructing a knowledge space by querying an expert assume that the domain of questions is known in advance, and that it is fixed during the whole query process. The outcome of these procedures is a knowledge space on the questions in that domain. If the original domain is extended with new questions, a new knowledge space on the extended domain can be produced by expert query. Since in this case a knowledge space for the original domain already exists, the available information can be used to extend the existing space in an efficient way, thus avoiding to apply expert query from scratch. Existing procedures do not provide an explicit way to use such information. Although these procedures can be adapted to this purpose, in this paper a new query algorithm that is specifically tailored for the problem above mentioned is presented.