An alternative formulation of the Fock-space coupled-cluster method using the hole-particle model spaces that fully exploits valence universal hierarchy of solving the coupled-cluster equations is presented. Formalism employs similarity transformations to separate eigenvalue problems for valence sectors with different numbers of quasiparticles but the same number of particles and that leads to certain simplifications in comparison with the previous formulations. These simplifications appear in the higher sectors that recently have been a subject of growing interest. The linked-cluster theorem is proven for the method.