Abstract: We present a bunch of novel phenomena stemming from the pair spin-orbit interaction (PSOI), which does not rely on structure inversion asymmetry but instead arises from Coulomb fields of interacting electrons in materials with a strong Rashba effect. First, PSOI can induce p-wave superconducting order without the need for any mediators of attraction. Depending on the sign and strength of the PSOI coupling, two distinct superconducting phases emerge in 3D systems, analogous to the A and B phases observed in superfluid He3. In contrast, 2D systems exhibit p_x \pm i p_y order parameter, leading to the time-reversal-invariant topological superconductivity. Second, a sufficiently strong PSOI can induce ferromagnetic ordering. It is associated with a deformation of the Fermi surface, which eventually leads to a Lifshitz transition from a spherical to a toroidal Fermi surface, with a number of experimentally observable signatures. Finally, in sufficiently clean Rashba materials, ferromagnetism and p-wave superconductivity may coexist. This state resembles the A1 phase of He3, yet it may avoid nodal points due to the toroidal shape of the Fermi surface.