Earthen Exposure: river guide
Check out the link... this guy has lined up the best list of overnighters that I have seen in North America. Of note... the utter lack of overnighters in Colorado for the most part. Yeah, you can pack gear and camp out on day runs, but its not the same feel and adventure as a "real" mutiday.
If you really want class IV multiday... you should probably scratch CO off your requirements and think Idaho or California.
While its true that many rapids on runs like the black canyon, upper taos box or big south are class IV and you can walk the class V, the folks I typically see running these as overnighter are class V boaters. You will likely never hear a class IV crew saying around the campfire... "we should go do an overnight on the big south".
Also, many folks who self support, especially when they are getting started are more comfortable on water a 1/2 grade or so below their normal river grade. Loaded boats and wilderness bring extra risk that makes you extra cautious.
Upper A sounds like its one of the few CO runs that fits the bill.