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Alvar The barnes coppers go down to 300gr.
See below the Double tap ammo that advertises the rem mag ammo at 3000fps. Honking for a big bullet. They don't seem to do it for the Rigby, but I'm sure...

I couldn't find it on the website so had to look them up.
A nice looking bit of kit I must say.

Id say the 400 grainers even the soft points a bit much on anything other than larger feral cattle beasts. Not much to start the bullets mushrooming.
From your comments it looks like you can reload?...

I cant comment so much. I have a 416 rem mag and only ever put one 400gr (came with the gun) down range.
My mate fired the other one and its the only gun he can remember that gave him a bruise...