Here's one example of the type of art you might do this with. The dark grey would be something flat, like suede or HD. Then the next special effect screen would be puff.
This is all screen print, simulating the look of an aged patch type work with an applique outline on type. But for the puff, you would just take that type separation of white, (choke it) so that when the puff does expend, it still sort of stays within the same area. Same for printing colors over puff. I'd done sim process fades and textures over puff. It washes out the color intensity but it works.
You don't want to puff the white of the type and the red fill also, since that feels overkill. People like to feel the intense differences of an outline, or just a solid puff of the type, not both. and it's good to break up the art so that the print is pliable as well. Large open areas of texture like you see here in that dark grey would work. You could puff that...as apposed to puffing anything else.