Post Processing OpenGL Framebuffer Practices

Right now, for post processing, I have a framebuffer that I’m drawing to the screen stretched over a quad with a special shader that does FXAA. My question is, is there any way to re-write the framebuffer to memory with a certain shader? Can you draw a framebuffer to itself? My main goal is to have one shader for FXAA and one for Vignette, and I want to have them in separate shaders, and have a modular system for post-processing shaders (it’s a game engine).

So is there any way to re-write a frambuffer to memory with a specific shader?

Thanks in advance.