The VIP-2 (VIolation of the Pauli Exclusion Principle) experiment conducted at the Gran Sasso underground laboratory (LNGS) of INFN is searching for possible tiny violations of standard quantum mechanics in copper atoms with extremely high sensitivity. We investigate atomic transitions with precision X-ray spectroscopy in order to test the Pauli Exclusion Principle (PEP) and therefore the spin-statistics theorem. We present the experimental method for the search for "anomalous" (i.e. Pauli-forbidden) X-ray transitions in copper atoms, produced by "new" electrons, which could have a tiny probability to undergo a Pauli-forbidden transition to the 1s ground state already occupied by two electrons. We describe the VIP-2 experimental setup and its recent optimisations. Presently VIP-2 is taking data at LNGS. The goal of VIP-2 is to test PEP for electrons with unprecedented accuracy, down to a limit in the probability that PEP is violated at the level of 10−31 (and using a more elaborate analysis even 10−40). We present current experimental results.