In this study, an extension on the previously reported status of the COllaborative Carbon Column Observing Network's (COCCON) calibration procedures incorporating refined methods is presented. COCCON is a global network of portable Bruker EM27/SUN FTIR spectrometers for deriving column-averaged atmospheric abundances of greenhouse gases. The original laboratory open-path lamp measurements for deriving the instrumental line shape (ILS) of the spectrometer from water vapour lines have been refined and extended to the secondary detector channel incorporated in the EM27/SUN spectrometer for detection of carbon monoxide (CO). The refinements encompass improved spectroscopic line lists for the relevant water lines and a revision of the laboratory pressure measurements used for the analysis of the spectra. The new results are found to be in good agreement with those reported by Frey et al. (2019) and discussed in detail. In addition, a new calibration cell for ILS measurements was designed, constructed and put into service. Spectrometers calibrated since January 2020 were tested using both methods for ILS characterization, open-path (OP) and cell measurements. We demonstrate that both methods can detect the small variations in ILS characteristics between different spectrometers, but the results of the cell method indicate a systematic bias of the OP method. Finally, a revision and extension of the COCCON network instrument-to-instrument calibration factors for XCO₂, XCO and XCH₄ is presented, incorporating 47 new spectrometers (of 83 in total by now). This calibration is based on the reference EM27/SUN spectrometer operated by the Karlsruhe Institute of Technology (KIT) and spectra collected by the collocated TCCON station Karlsruhe. Variations in the instrumental characteristics of the reference EM27/SUN from 2014 to 2017 were detected, probably arising from realignment and the dual-channel upgrade performed in early 2018. These variations are considered in the evaluation of the instrument-specific calibration factors in order to keep all tabulated calibration results consistent.