I'd love to have one and contacted Browning about availability. Their response was there are no new production BLR rifles in 358 due to lack of sales orders and demand. Used is going to be your only avenue or perhaps a rebore of an 308 BLR.
Love mine! Steel receiver and straight grip. I use Hornady 180gr Single Shot pistol bullets and IMR4895 powder. Stays under 1-1/2" for 3 shots at 100 yards all day. It also likes the Hornady 200rgr spire point and H335 powder for 2,550fps. I never chronographed the 180's.
Mine is a BLR 81 steel frame . It is one of the four rifles that I absolutely would not part with. I would not care to have one of the alloy framed ones they sell now but the steel framed ones are a great rifle.
Grumpy old man with a gun.....Do not touch . Better to be judged by 12 than carried by 6. Don't bother my monument and I'll leave yours alone.