I have an old application that uses frames (not iframes) was was written back in the IE6 days so it runs in quirks mode.
Is it possible (Using IE 7 or 8) to have one
I'm not sure if this helps, but according to the Mozilla Dev center Firefox makes it's quirksmode decisions based on doctype only.
https://developer.mozilla.org/en/Mozilla's_DOCTYPE_sniffing
You'll notice using the old frameset doctype triggers "almost standards" mode, which could show up as quirksmode.