I have to correct myself.
After playing around a bit I have found some way. Set units to Architectural and precision to 1/16", grid spacing to 0.0625.
You can switch to Engineering after that, but the main grid will then consist of 10 1/16" units.
You may experiment yourself a bit with the settings.
If you are zoomed out too much so it's too dense for 16 sections to fit into one inch, less are shown. As soon a there is enough space it stays at 16 sections.