We discuss the quantum dot-ring nanostructure (DRN) as canonical example of a nanosystem, for which the interelectronic interactions can be evaluated exactly. The system has been selected due to its tunability, i.e., its electron wave functions can be modified much easier than in, e.g., quantum dots. We determine many-particle states for Ne = 2 and 3 electrons and calculate the 3- and 4-state interaction parameters, and discuss their importance. For that purpose, we combine the first- and second-quantization schemes and hence are able to single out the component single-particle contributions to the resultant many-particle state. The method provides both the ground- and the first-excited-state energies, as the exact diagonalization of the many-particle Hamiltonian is carried out. DRN provides one of the few examples for which one can determine theoretically all interaction microscopic parameters to a high accuracy. Thus the evolution of the single-particle vs. many-particle contributions to each state and its energy can be determined and tested with the increasing system size. In this manner, we contribute to the wave-function engineering with the interactions included for those few-electron systems.