Distinguishing Internally Club and Approachable on an Infinite Interval

Krueger showed that PFA implies that for all regular $\mathrm{\Theta }\ge {\mathrm{\aleph }}_2$, there are stationarily many $[H(\mathrm{\Theta }){]}^{{\mathrm{\aleph }}_1}$ that are internally club but not internally approachable. From countably many Mahlo cardinals, we force a model in which, for all positive $n<\omega$ and $\mathrm{\Theta }\ge {\mathrm{\aleph }}_{n+1}$, there is a stationary subset of $[H(\mathrm{\Theta }){]}^{{\mathrm{\aleph }}_n}$ consisting of sets that are internally club but not internally approachable. The theorem is obtained using a new variant of Mitchell forcing. This answers questions of Krueger.