In previous experiments on x-ray parametric down-conversion (XPDC), we successfully resolved the splitting into highly asymmetric (i.e., x-ray and EUV) photon pairs. We observed remarkable scattering features that revealed the hybridization of this EUV photon with matter, thus forming an EUV polariton. In this way, XPDC provides a rare and novel insight into strong light-matter coupling in the EUV regime. Here, we aim to extend this capability to the class of ‘exciton polaritons’: Exploring XPDC for the first time near a core-shell resonance, we expect the down-converted EUV photon to hybridize strongly with this electronic resonance. We propose to use lithium triborate (LBO), which is known for its high optical nonlinearity, while also exhibiting two promising exciton resonances (i.e., before the K-edge of Boron and Lithium). We aim to observe EUV exciton polaritons at both resonances, obtaining unprecedented insights into their formation, life-time and electronic structure.