Ultracold atomic gases have emerged as ideal quantum simulators, as they enable experimentalists to study the interplay between the properties of a quantum many-body system and the interactions between its constituents with unmatched accuracy. However, in spite of impressive progresses, an atomic quantum simulator of highly correlated fermionic matter, able to address both phenomena of exotic superfluidity and itinerant ferromagnetism, still awaits experimental demonstration. Such a system needs to be built from the ground-up by carefully harnessing the underlying few-body physics. In CriLiN I will develop and test a new kind of Atomic Quantum Simulator of unequal-mass spin-1/2 fermions with long-range, multi-body resonant interactions. In order to do so, I will exploit the still unexplored 6Li-53Cr Fermi-Fermi mixture which, thanks to its special mass ratio of M/m=8.8, exhibits unique few-body properties that strongly favour the many-body phases of our interest. Indeed, on the “molecular side” of an interspecies s-wave Feshbach resonance, the Cr-Li system supports a real (virtual) stable universal trimer (tetramer) state, while benefiting from quantum-interference induced suppression of three-body recombination processes. At the few-body level, this will allow for the first time to resonantly tune multi-body, long-range p-wave interactions. At the many-body level, this will allow both to investigate Stoner's model of itinerant ferromagnetism and to greatly enhance the possibility to attain elusive superfluid regimes or topologically non-trivial p-wave superfluids. In CriLiN I will: (i) realize a degenerate 6Li-53Cr Fermi-Fermi mixture and identify intra- and inter-species Feshbach resonances suitable for our simulator; (ii) unveil and characterize stable cluster states and exploit them to resonantly tune three- and four-body elastic interactions; (iii) demonstrate the suppression of inelastic pairing processes in repulsively interacting mixtures.