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Super-Eddington accretion periods are expected to be extremely important to explain the fast growth of the first supermassive black holes. However comma among all accretion modes comma this phase is still the least understood one comma and it is still largely debated what are the physical properties of the accretion flow and of the X-ray source at very high accretion rates. We propose here a systematic broad-band X-ray study of super-Eddington AGN at z<0.1 by simultaneously observing three sources with NuSTAR and XMM.These three AGN have the highest Eddington ratios in the SEAMBHs sample comma which contains exclusively objects with black hole masses estimated from reverberation mapping comma making the Eddington ratio estimates extremely reliable.