Yup, plenty of 4×4 shuttling to be done right in and around Crested Butte! Grab a map, look for the 4×4 roads, and the singletrack dropping off of them. No end of options.
Doctor Park is a great trail and a 4×4 shuttle could be useful, but you really only need a decent rig for the last mile or two, and it’s not truly burly 4×4 road. Most moderately high clearance vehicles can make it.
That said, plenty of options if you want to get adventurous.