My mesh does not seem to tessellate beyond a certain point. I can only further increase the resolution by pre-tessellating the base geometry. After some research, I found out that the tessellation is limited to 8 subdivision levels.
I found this source which allows me to change the maximum tessellation, but it appears to be outdated.
The source wants me to modify a usf file where the maximum tessellation variable is stored, but I can only find ush files.