Localizing Global Effects

Certain effects are set up for the whole of the OpenGL application; for example, things that are set up in InitGL. Like enabling Depth Testing, and changing the way the backs and fronts of polygons appear. In something like Tutorial 09, you are required to disable Depth Testing, among other things, to make the Bitmaps blend correctly. If I were to want to display something, at the same time on the same screen in the same render, but with Depth Testing enabled (for example, if I wanted to do Blending), how would I configure it so that I could do both? Another example is, like in Tutorial 11, it renders a flag (a literal flag, to be more specific, not a boolean flag) with global settings (not state settings like Color or Texture) to display the front of the polygons as solid but the back of the polygons as lines. If I wanted to display something with other options, perhaps solid on both sides, or lines on both sides, or some other combination, but I wanted to display it at the same time, on the same render, as the Flag, how would I localise the global effect? Thanks for your help.