All-electron relativistic self-consistent-field (RSCF) method is extended to treat linear molecules with many open shells where each open shell has different symmetry. The extension is based on the omega-omega coupling scheme and the projection operator technique. All-electron RSCF calculations with Slater-type basis functions have been performed for the CO molecule with a closed-shell (CO, 1SIGMA+), one open-shell (CO+, 2SIGMA+), and two open-shell (CO, 3PI and 1PI) configurations. Basis set studies of the RSCF method indicate that the calculations using basis sets of double-zeta quality produce correct trends and reasonable magnitudes of relativistic effects on total and orbital energies, ionization and excitation energies, and pi orbital splittings.