I am in the process of laying down multiple thin wipe on coats of poly
to a project.

The first half dozen coats were done in gloss. Then I switched to
semi-gloss for the final two coats. The first coat of semi-gloss,
still left the wood with a pretty high sheen.

Will the semi-gloss (i.e. less sheen than gloss) nature continue to
build with additional coats of semi-gloss additional or will I need to
go to satin if I want the surface to be less shiny?

i.e. is the non-gloss sheen just determined by the top coat or does it
build across multiple coats?