We characterize the 3-stratifiable theorems of NF as a 3-stratifiable extension of NF3: and show that NF is equiconsistent with TT plus raising type axioms for sentences asserting the existence of some predicate over an atomic Boolean algebra.
Crabbé, M. (2000). The rise and fall of typed sentences. The Journal of Symbolic Logic, 65(4), 1858-1862. https://doi.org/10.2307/2695082 (Original work published 2000)