Yes but you will need a tapered expander from Redding and you will probably need to do it in two steps.
If it were me, I would neck it up to 7mm(just under half way) or to 308(just over half way) and then anneal the case necks before stepping them up to 338.
I would only anneal the case neck and avoid the shoulder to help prevent any collapsed shoulders.
You may be able to do both steps before annealing and if so great but make sure you anneal after you get to 338 or you will have some case neck splits upon firing.
Be sure to deburr the inside of the case mouth very well and use plenty of lube on that expander.
With the tapered expanders and the short case length of the BR you may run into some issues with clearance of the expander and case web. Watch for this so you do not pop a decapping stem by bottoming out in the case.
Let us know how it turns out.
Kirby Allen(50)