An inaccessible cardinal $\kappa$ is supercompact when $(\kappa, \lambda)$-ITP holds for all $\lambda\geq \kappa$. We prove that if there is a model of ZFC with infinitely many supercompact cardinals, then there is a model of ZFC where for every $n\geq 2$ and $\mu\geq \aleph_n$, we have $(\aleph_n, \mu)$-ITP.
"Strong tree properties for small cardinals." J. Symbolic Logic 78 (1) 317 - 333, March 2013. https://doi.org/10.2178/jsl.7801220