An experiment has demonstrated that controlling the Xe occupancy of each pore in 12 steps confi gures a self-assembled array of quantum boxes: the Pauli repulsion imposed by Xe atom(s) modifies the quantum box states and, notably, adds an additional confining dimension to the coupled quantum boxes. Xe of purity 99.99% was dosed onto the sample placed in the STM operated at 4.2 K, with the cryoshields open and the leak valve being in line-of-sight with the sample. The sample was exposed to 120 L (Langmuir) of Xe resulting in the increase of the sample temperature to 9 K. The STM measurements performed after cooling the sample back to 4.2 K revealed different numbers of Xe atoms adsorbed in the pores as well as at the domain boundaries and step edges. To avoid modification of the condensates via interaction with the tip, the sample bias was selected within a range of -10 mV to -80 mV, whereas the tunneling current was set within the range of 5?50 pA. The work demonstrates that the simplified picture of the emergence of the confined states from the 2D electron gas needs to be extended to include potential confinement effects in the out-of-plane dimension and underpins the well-established fact that the observed physical effects at interfaces are not by nature strictly 2D.