Your articulation is not very clear so it’s hard for me to understand your situation.
Anyway I think studying how the base template works might help you.
This page with a nice video helped me a lot at least:
If your layouts will differ a lot you can for example just have the basic HTML HEAD BODY structure defined in the baseof.html and define everything else in specific layouts.
See index.html uses the baseof.html the same way single.html uses baseof.html (baseof.html defines places for blocks insertions while the blocks are defined in index and single and other specific layouts) - so you probably can’t make index.html use single.html as its base because single.html is no base at all. But you can make a partial/commonpartofyourlayouts.html and call it both from index.html and single.html.
Plus one more thing to study - lookup order for the homepage layouts: