Using a scaled Kohn-Sham formalism, we examine three heavy- and light-hole excitons, respectively, in three coupled quantum dots to study the effects of competition involving the electron-electron and hole-hole interactions between excitons, the electron-hole interaction within excitons and the effective masses. The particle-particle interactions play dominant roles in determining the configuration of the excitons in the coupled dots. In the absence of an external electric field, the two lowest (occupied) energy states of the heavy-hole excitons are degenerate, and the excitons have an equal probability of residing in either of the two side dots. The corresponding states of the light-hole excitons exhibit nondegenerate character and the lowest energy exciton is confined predominantly to the centre dot. Under a weak dc electric field, both the heavy- and light-hole excitons form direct excitons which are localized in the side dots. For large values of the electric field, we find that the electrons associated with the excitons become ionized as a result of strong confinement by the field and the electron-electron repulsion between excitons before the excitons can be transformed into indirect excitons. This result is in contrast to the conclusion that a single exciton in a double-quantum-well structure will be transformed into an indirect exciton in real space when it is subjected to large fields. Furthermore, we suggest that the wave function overlap between interacting excitons may diminish significantly the increase in excitonic lifetime predicted for a single exciton in two coupled quantum dot systems, implying that it may be difficult to make use of several excitons in coupled structures for nonlinear devices.