Multicenter multielectron integrals appearing in the study of multielectron properties of atomic and molecular systems are evaluated using one-range addition theorems in terms of complete orthonormal sets of ϕα-exponential type orbitals (ϕα-ETO, α = 1, 0, −1, −2, …) for ϕα-ETO and Coulomb-Yukawa like correlated interaction potentials (CIP) introduced by the author. The final results are especially useful for the computation of arbitrary multicenter multielectron integrals that arise in the Hartree-Fock- Roothaan (HFR) approximation and also in the explicitly correlated methods based upon the use of ϕα-ETO as basis functions.