It is well known that the critical temperature of multigap superconducting three-dimensional (3D) heterostructures at atomic limit (HAL) made of a superlattice of atomic layers with an electron spectrum made of several quantum subbands can be amplified by a shape resonance driven by the contact exchange interaction between different gaps. The T C amplification is achieved tuning the Fermi level near the singular nodal point at a Lifshitz transition for opening a neck. Recently high interest has been addressed to the breaking of inversion symmetry which leads to a linear-in-momentum spin-orbit induced spin splitting, universally referred to as Rashba spin-orbit coupling (RSOC) also in 3D layered metals. However the physics of multigap superconductivity near unconventional Lifshitz transitions in 3D HAL with RSOC, being in a non-BCS regime, is not known. The key result of this work getting the superconducting …