Recent evaluations of neutron cross-section covariances in the resolved resonance region reveal the need for further research in this area. Major issues include declining uncertainties in multigroup representations and the proper treatment of scattering radius uncertainty. To address these issues, the present work develops a formalism and computer code based on a multilevel Breit-Wigner formula, extending the previous work based on the kernel approximation, using resonance parameter uncertainties from the Atlas of Neutron Resonances. Analytical expressions derived for average cross-section uncertainties in the arbitrary energy bin along with their sensitivities provide a fundamental tool for determining the cross-section uncertainties. The role of resonance-resonance and resonance-potential scattering correlations is studied. As a test case, we apply this approach to estimate (n,γ) and (n,el) covariances for the structural material 55Mn and compare the results with those from the previous kernel approximation.