The single-reference (SR) configuration interaction (CI) method is nowadays rather rarely used in quantum-chemical calculations. The reason is that the method is not competitive with the coupled-cluster (CC) approach that uses the same number of parameters but is size-extensive and more accurate. The accuracy of the CI method can be increased by applying size-extensivity a posteriori corrections but even that does not make the SR-CI method much more attractive. The CI scheme has, however, one important advantage over the CC one. Due to its formal simplicity, the SR-CI approach can be easily generalised to the multi-reference (MR) case while such a generalisation for the CC method turned out nontrivial. Two basic MR-CC formulations are formally complicated, numerically demanding, vulnerable to intruder states, and sensitive to the problem of multiple solutions. Contrary to that the MR-type CI schemes are among very few methods that are used in routine calculations for systems requiring a MR description. The problem of improving the MR-type CI results by applying an a-posteriori correction is in this context very appealing. In the paper, we discuss different types of corrections trying to show that the one based on the SR cluster expansion is both well theoretically justified and reliable in numerical applications. That is illustrated on model CI calculations of SR and MR type.