The cluster degree of freedom has often been introduced to interpret the spectroscopic properties of exotic nuclei including α-conjugate nuclei and a series of nuclei above double shell closures. In this study, we have systematically investigated the so-called unnatural-parity states and higher-lying bands for the typical nucleus 212Po based on the coupled-channels formalism, which allows the excitation of the core 208Pb plus multiple interactions. A general agreement between our calculations and the available data was obtained for the parity doublet bands and electromagnetic transition probabilities. Encouraged by that result, the present framework is extended to describe the nuclear properties of 216Rn with the configuration of heavier cluster plus core 208Pb. Reasonable predictions of reduced transition rates and great improvement of energy bands for 216Rn were achieved beyond the treatment of the binary cluster-core model (BCM) without the coupling of cluster states, reconfirming the reliability of the present coupled-channels formalism. It is hoped that the current study can yield a new perspective on understanding the role of cluster degrees of freedom in heavy nuclei.