As of IE11, document modes are deprecated but continue to work.
http://msdn.microsoft.com/en-us/library/ie/dn384051%28v=vs.85%29.aspx
I don't think they've decided (as of Jan 2014) exactly when it will be removed entirely (all at once in IE12 or gradually). Probably it depends on the amount of resistance people give to the deprecation status.
I also maintain a big internal application built between 2000-2004 or so. We have been banging the drum of needing to redo parts of the old site for years but new features are always priority. Personally I am bracing for hitting a brick wall with IE12 later this year, but hoping there will be a gradual removal.
Edit: in early 2015 I've been reading that Windows 10 will ship with 2 browsers: code-name Spartan for the latest/greatest, and IE for legacy support. It's worth googling "Windows Edge" (formerly "Windows 10 Spartan") if you're interested in this topic. Possibly this is their answer for how to continue supporting older internal corporate web apps, without compromising the main consumer browser.
Hopefully the legacy browser doesn't fall behind the newer support, since our internal app is a mix of new and old web pages. It would suck if our company couldn't use the latest web technologies of 2016, 2017, etc., because older pages force our users to use the legacy browser. :(