We study the effects of higher-order electronic correlations in the systems with particle-hole excited states using a relativistic hybrid method that combines configuration interaction and linearized coupled-cluster approaches. We find the configuration interaction part of the calculation sufficiently complete for eight electrons while maintaining good quality of the effective coupled-cluster potential for the core. Excellent agreement with experiment was demonstrated for a test case of La3+. We apply our method for homolog actinide ions Th4+ and U6+ which are of experimental interest due to a puzzle associated with the resonant excitation Stark ionization spectroscopy method. These ions are also of interest to actinide chemistry.