We use ab initio calculations to study the role of stacking faults in connecting the high-temperature B2 and the theoretically predicted low-temperature B33 NiTi phases. In contrast with prior work, we describe the B2 -> B33 phase transformation in terms of alternate bilayer shifts by 1/2[100] on the (011)(B2) plane, obtaining a viable pathway; the same mechanism could also work with the B19 parent phase. We then examine B33-like structures built from alternate stacking sequences of B19 bilayers, constructed to have monoclinic tilt angles close to the experimentally reported NiTi B19' martensite, and find four low-energy stacking-fault variants with energies 5.8-8.5 meV/atom above the calculated B19' martensite structure, suggesting that such structures might appear as a part of the NiTi martensite phase at low temperatures. Investigating further the occurrence of specific coordinated planar shifts in NiTi systems, we report a dynamically stable NiTi B27 phase and find that it is only 1.2 meV/atom above the calculated B33 ground-state structure, thus having a potential to also play a role in NiTi martensitic phase transformation.