Broadly speaking, the calculation of core spectra such as electron energy loss spectra (EELS) at the level of density functional theory (DFT) usually relies on one of two approaches: conceptually more complex but computationally efficient projector augmented wave based approaches or more straightforward but computationally more intensive all electron (AE) based approaches. In this work we present an alternative method, which aims to find a middle ground between the two. Specifically, we have implemented an approach in the multiwavelet madness molecular DFT code that permits a combination of atoms treated at the AE and pseudopotential (PSP) level. Atoms for which one wishes to calculate the core edges are thus treated at an AE level, while the remainder can be treated at the PSP level. This is made possible thanks to the multiresolution approach of madness, which permits accurate and efficient calculations at both the AE and PSP level. Through examples of a small molecule and a carbon nanotube, we demonstrate the potential applications of our approach.