Hi Tex, and welcome to DHC!
Here's what I can tell you about your gun. To my knowledge, the Model 11 was discontinued in 1948 with the introduction of the 11-48. Remington states that it is safe to shoot steel through any of their guns built after 1950 with any choke modified or more open. That would make it seem that your gun shouldn't be able to shoot steel. But, there's more. CIP (who's regulations have no bearing on American Guns) has a recommendation for shooting steel through older guns in rather dubious condition. Basically, they state that if you keep the load to 1 1/8oz or less, the muzzle velocity to 1400fps or below, the shot size to US #4 or smaller and the choke to modified or more open, you shouldn't have any problems. The one thing about that charge weight and muzzle velocity is that you have a little leeway. CIP's actual recommendation is stated as the momentum, or the charge weight multiplied by the velocity. Furthermore, the velocity is measured at some 2.5 meters. Boiling CIP all down, here's my take. Your gun is probably a 2 3/4inch gun, so if you use the Remington Nitrosteel 1 1/4oz, 1350fps loads, you shouldn't have any problems. Given that your gun was built to a much tough standard that the guns CIP is talking about, you could probably increase the pellet size a bit. You should have no trouble shooting #3 steel, whatsoever.
Tom Roster has published that you can shoot modern steel through any shotgun, regardless of choke, provided that the gun is in good condition. He bases this on the fact that some 15 or 20 years ago he developed and patented a wad that provided protection against barrel damage. The one caveat is that in come cases, the barrel can develop a bulge right behind the choke area. This bulge is completely cosmetic and will not effect the gun's performance, nor will it be of any danger.
That's the published part, now here's the personal experience part. I had a friend of mine that inherited a Model 11 from an old duck hunter when he passed on. My friend used that gun for years shooting 1 1/4oz steel #2s at 1350fps and steel #1s for geese. He finally retired the gun two years ago because it just wore out (he and the gun's previous owner did a lot of waterfowling.) My friend was also not the most religious when it came to cleaning and maintenance. If the gun went bang and cycled when he pulled the trigger, he was happy. But, I can tell you for a fact, that gun, after a steady diet of steel loads, had no changes to the barrel. No walnut, no scoring, and no wearing at the choke as far as we could see.
So that's about it. If it were me, I'd shoot 1 1/4oz of #3s at 1300 to 1400fps and never look back. But it's a decision that only you can make. Hope this helps some.
I feel slightly sorry for a man who has never patterned his gun, who has no idea how far his chosen load will retain killing penetration. But I'm extremely sorry for the ducks he shoots at beyond the killing range of his gun and load - Bob Brister