FAA has been adding alternate missed approach procedures to ILS
approaches to allow the ILS procedure to still be flyable even when the
VOR or VORTAC used in the procedure is INOP. They don't normally publish
this on the procedure though. I like it though, because then a NOTAM
doesn't need to be sent listing the alternate missed approach procedure
when BRV is INOP.
If there are a lot of military TACAN equipped aircraft that use this
particular procedure, then having the other missed approach procedure
published is required, since TACAN aircraft cannot hold directly over a
VORTAC or TACAN (unless they also have a VOR). In that case, it would
normally be published as shown on this procedure at Chippewa MI;
http://www.naco.faa.gov/d-tpp/0405/00810I16.PDF

Brad Z wrote:

http://www.naco.faa.gov/d-tpp/0405/09743IL33.PDF

I haven't come across an approach with two separate missed approach
procedures before. Is this even remotely common?

I think I'll add this to my instrument students' training regiment due to
some additional interesting features- teardrop course reversal, intersection
identification using ndb bearings (not using DME), and a lot of stuff to
brief. Some of the approaches down here in central VA are pretty boring.