Inter-layer excitons (IXs) in hetero-bilayers of transition metal dichalcogenides (TMDs) represent an exciting emergent class of long-lived dipolar composite bosons in an atomically thin, near-ideal two-dimensional (2D) system. The long-range interactions that arise from the spatial separation of electrons and holes can give rise to novel quantum, as well as classical multi-particle correlation effects. Indeed, first indications of exciton condensation have been reported recently. In order to acquire a detailed understanding of the possible many-body effects, the fundamental interactions between individual IXs have to be studied. Here, we trap a tunable number of dipolar IXs ( N ~ 1–5) within a nanoscale confinement potential induced by placing a MoSe 2 –WSe 2 hetero-bilayer (HBL) onto an array of SiO 2 nanopillars. We control the mean occupation of the IX trap via the optical excitation level and observe discrete sharp-line emission from different configurations of interacting IXs. The intensities of these features exhibit characteristic near linear, quadratic, cubic, quartic and quintic power dependencies, which allows us to identify them as different multiparticle configurations with N ~1–5. We directly measure the hierarchy of dipolar and exchange interactions as N IX increases. The interlayer biexciton ( N = 2) is found to be an emission doublet that is blue-shifted from the single exciton by Δ E = (8.4 ± 0.6) meV and split by 2 J = (1.2 ± 0.5) meV. The blueshift is even more pronounced for triexcitons ((12.4 ± 0.4) meV), quadexcitons ((15.5 ± 0.6) meV) and quintexcitons ((18.2 ± 0.8) meV). These values are shown to be mutually consistent with numerical modelling of dipolar excitons confined to a harmonic trapping potential having a confinement lengthscale in the range ℓ ≈ 3nm. Our results contribute to the understanding of interactions between IXs in TMD hetero-bilayers at the discrete limit of only a few excitations and represent a key step towards exploring quantum correlations between IXs in TMD hetero-bilayers.