Sure. You can put in as high as the bottom of Platoro Reservoir and I have paddled as far down as the South Fork Conejos confluence. You can go further, but I've heard there used to be a fence or two across the river. This is not an extremely long run (probably on the order of 10? miles), but there is some prime real estate for camping, or you can reserve a site at the Lake Fork Campground.
There are also some options for multi-day floats on the Rio Grande in Colorado.
When I run the Conejos I often combine it with stuff in the Pagosa area (East Fork San Juan, Mesa Canyon, Piedra). Rio Grande and Lake Fork Gunnison are not far away either.
The Conejos certainly doesn't have the mileage to warrant a true multi day float. HOWEVER, I have enjoyed many overnight trips on Browns Canyon of the Ark and it's a similar length. Plus everything on the west bank of the Conejos is South San Juan Wilderness. You could spend several days hiking and exploring the area.
The best section of the Upper Rio Grande to overnight is the Box Canyon below Rio Grande Reservoir. Again, it's not an overly long run, but the south shore borders the Weminuche Wilderness... also providing ample opportunity for camping and exploration. The biggest downfall to this area is that it burned a few years back. I haven't been there since, but hopefully the forest is starting to revegetate itself.
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