To jointly resolve inter-slice leakages and in-plane aliasing in undersampled SMS imaging, we proposed a novel, one-step solution for SMS-reconstruction optimally exploiting variable-density(VD) sampling from generalized 3D Fourier encoding perspective. Extended controlled aliasing is performed by upsampling VD sampled data in the <jats:italic>k</jats:italic><jats:sub>z-</jats:sub>direction. A slice-specific null space operator is learned using extended self-calibration including CAIPI slices and in-plane images. Aliasing artifacts are jointly resolved in <jats:italic>k</jats:italic><jats:sub>y-</jats:sub>and <jats:italic>k</jats:italic><jats:sub>z-</jats:sub>directions by balancing null space consistency with a low rank prior while enforcing slice-specific VD-sampled data in 3D k-space. We demonstrated the proposed method outperforms competing methods at SMS=3,R=2 in head and knee.