I wish it was all Multi-use. A big push back on the Blair Creek section from Sierra Club and Roger Pryor Backcountry have held off on bike access and even alternative trail options(Note - There is something of an Equine bypass in Roger Pryor near Powder Mill/North of Hwy 106.) The National Park Serivce and MDC have pushed back on bike and equine access to the Current River Section at this time.
There is some gravel road connectivity that can make for a 230 mile thru trip. Basically connect from Hwy P at 72 (Karkahgnee southern Terminus) down to Hwy 60 at Van Buren. It's quite a stretch but there are plenty of roads. Pavement will be required closer to Van Buren. Consider staying East of the Current River.
These connected sections open from North To South ( Courtois, Including Berryman Trail, Trace Creek, John Roth Memorial Middle Fork, Karkahgnee).
Blair Creek and Current River Sections are closed to bike.
Between the Rivers, Eleven Point sections are open.
Other multi-use sections - Victory, Wappapello, and Marble Creek sections are open to bikes.