We prove that the extent partitions of a formal context K := (G,M,I) can be constructed from the box extents of it, which form a complete atomistic lattice. K is called a one-object extension of the subcontext (H, M, J) if it is obtained by adding a new element with attributes in M to the set H. We investigate the interplay between the box extents of (H, M, J) and those of its one-object extension K, and describe those extent partitions of (H, M, J) which can be extended to K.