For instance, there's a pyramid 5 post already in existence, and I want to quote the middle post which is the 3rd
You can always follow a quote if you want to do that, just click on the quote from section of the quote this will direct you to the original quote without any edit , you can edit the particular quote from there.
Note: if the post is having just only "quote" as label without "quote from: ...." then the user didn't include the link to that quote /maybe it's just an external quote from websites/Ai ...... unless you're trying to include the user comment too(I.e from where you found the quote you followed), then you have no choice than to use the normal pattern of editing unless there's a better way to implement that.
Check:
hd49728 post on this thread
The only disadvantage I see in this is that it will discourage the organic flow of conversation. You could reply on point to a particular post and someone will quote only your post which might be off context if it stands alone.
It still depends on the user quoting such post, if a user wants to quote just your post and your post is having multiple quotes within, he can still do else if he wants to quote it including other quotes you added he can still do that... there's nothing changing , it's not actually going to change how things are being done rather speeds up how it's being done for someone who wants to use it .