  Numerous numerical studies have shown that geminal-based methods are a
promising direction to model strongly correlated systems with low computational
costs. Several strategies have been introduced to capture the missing dynamical
correlation effects, which typically exploit \textit{a posteriori} corrections
to account for correlation effects associated with broken-pair states or
inter-geminal correlations. In this article, we scrutinize the accuracy of the
pair coupled cluster doubles (pCCD) method extended by configuration
interaction (CI) theory. Specifically, we benchmark various CI models,
including, at most double excitations against selected CC corrections as well
as conventional single-reference CC methods. A simple Davidson correction is
also tested. The accuracy of the proposed pCCD-CI approaches is assessed for
challenging small model systems such as the \ce{N2} and \ce{F2} dimers and
various di- and triatomic actinide-containing compounds. In general, the
proposed CI methods considerably improve spectroscopic constants compared to
the conventional CCSD approach, provided a Davidson correction is included in
the theoretical model. At the same time, their accuracy lies between the
linearized frozen pCCD and frozen pCCD variants.
