The spatial orbital formulations of block correlated coupled cluster (BCCC) theory with a general CASSCF reference function (CAS-BCCC in short) is derived and an efficient implementation of this approach at the four-block correlation level (abbreviated CAS-BCCC4) is reported. We have applied the CAS-BCCC4 approach to investigate energy barriers for several reactions (the ring-opening isomerization of the cyclopropyl radical, cyclobutene, cyclobutadiene, and bicyclo[3.1.0]hex-2-ene), spectroscopic constants in several multibond diatomic molecules (C-2, O-2, CO, and N-2), and singlet-triplet gaps in two diradicals (trimethylenemethane and oxyallyl). A comparison of CAS-BCCC4 results with the experimental data or other theoretical estimates shows that the present approach can provide very satisfactory descriptions for all the studied systems.