The new formulas have been established for the expansion and one-range addition theorems for the complete orthonormal sets of functions in coordinate, momentum, and four-dimensional spaces. These theorems enable us to derive the formulas for the overlap integrals over STOS, Psi(alpha)-ETOs, Phi(alpha)-MSOs, and Z(alpha)-HSHs which can be useful in the study of different quantum mechanical problems in both the theory and practice of calculations dealing with atoms, molecules, and solids when the coordinate, momentum or four-dimensional spaces employed. This work presents the development of our previous paper (I.I. Guseinov, J. Math. Chem., (2007) DOI: 10.1007/s10910-006-9154-1).