A core–corona decomposition of compact (neutron) star models was compared with the current mass–radius data of the outlier XTE J1814-338. The corona (which may also be dubbed the envelope, halo or outer crust) is assumed to be of Standard Model matter, with an equation of state that is supposed to be faithfully known and accommodates nearly all other neutron star data. The core, solely parameterized by its mass, radius and transition pressure, presents a challenge regarding its composition. We derived a range of core parameters needed to describe the current data of XTE J1814-338.