Kawai, Kerman, and McVoy have shown that a statistical treatment of many open channels that are coupled by direct reactions leads to modifications of the Hauser- Feshbach expression for energy-averaged cross section (Ann. of Phys. 75, 156 (1973)). The energy averaging interval for this cross section is on the order of the width of sin- gle particle resonances, 1 MeV, revealing only a gross structure in the cross section. When the energy-averaging interval is decreased down to a width of a doorway state, 0:1 MeV, a so-called intermediate structure may be observed in cross sections. We extend the Kawai-Kerman-McVoy theory into the intermediate structure by leveraging a theory of doorway states developed by Feshbach, Kerman, and Lemmer (Ann. of Phys. 41, 230 (1967)). As a by-product of the extension, an alternative derivation of the central result of the Kawai-Kerman-McVoy theory is suggested. We quantify the e ect of the ap- proximations used in derivation by performing numerical computations for a large set of compound nuclear states.