I have a custom stylesheet I call MyStyle and I am looking at some of the built-in stylesheets such as ReverseColor. So with a fresh notebook inheriting the ReverseColor stylesheet, I want to add in my MyStyle stylesheet so that it would be inherited too. So I copied and pasted Cell[StyleData[StyleDefinitions -> "MyStyle.nb"]] into the private stylesheet of this notebook. However, the changes did not apply. But if I copy and paste all of the individual styles from MyStyle into this private stylesheet, the changes take place. So that made me think that you can not inherit base definitions from more than one stylesheet. However, I have a notebook called "Sample Lab Exercise" (downloaded it from a Wolfram rep a few years ago) and noticed its private stylesheet is inheriting from "Default.nb" and "StyleMenuClear.nb" and has other individual styles below. Moreover, the edits from the second inherited stylesheet (StyleMenuClear) are taking effect.

So is there something special about the way StyleMenuClear.nb is put together (it seems to just add MenuSortingValue->None to several styles) or is there something I have to do in order to inherit base definitions from more than one stylesheet?

I also experimented and I see that if I start a default notebook and in the private stylesheet add Cell[StyleData["Text"],FontFamily->"Times"] and then in a second cell some other modification of the style Text, only the first one applies. So that made think that if you want to edit a style, you need to see if it has already been edited earlier and then add that edit to that cell (I am not sure if it matters whether an earlier occurrence of that style is explicitly listed or if it is being inherited from another stylesheet). Is that correct? If so, then I don't understand how Mathematica treats edits to styles such as Text (or any other already defined style) since they are already have definitions or edits in Default.nb and Core.nb or other stylesheet the notebook is inheriting base definitions from.