It is well known that the nuclear shell structure changes for the most exotic nuclei. One of the consequences of this phenomenon is the modification of the "classical" magic numbers, as experimentally observed at N = 20 and N = 28. Nevertheless, the mechanisms responsible for such changes are still under discussion and more experimental information is needed to better constrain the theoretical models. In these proceedings, we report on the discovery and the experimental study by precise spectroscopy experiments of the 0 2+ state in 34Si and 44S. The 34Si is located between the magic spherical 36S and the deformed 32Mg, member of the so-called island of inversion, whereas 44S is located between the magic spherical 48Ca and the deformed 42Si. Therefore, the structure of these nuclei, and in particular the phenomenon of shape coexistence, is of crucial importance to understand how the intruder configurations progressively dominate the ground state structure of the most exotic nuclei at both N = 20 and N = 28.