Over time I've had every version of the chewing and untrustworthy Doberman puppy that could possibly exist.
The very best one was my now 9 year old--he had free run of a small gated off area when he was about six months old. He had one bout of drywall tasting but it was in an area that was practically invisible and easily patched--only took a bit of patching compound and about 5 minutes. He was, however the dog who removed an entire strip of wall paper from behind a door (a door that stayed open all the time so it took a long time for me to notice it) he did a pretty tidy job and I thought that I might be able to put him to work as a wall paper stripper but he was pretty slow at it.
He was the BEST--the worst has only just at four been allowed to be loose--he was also the dog who had no blankets in his crates from 8 or 9 months until about six months ago because he not only shredded them but ate them as well--shredding wasn't so bad but the eating could have ended up with a very expensive surgery to unblock him--I wasn't about to wait to see which came first--no blanket eating or an intestinal blockage.
And I've had everything inbetween--dogs that chewed on anything wood, dogs that stole all the cat toys from the basket they were kept in (supposedly out of the reach of bad dogs) dogs who did fine as long as you didn't let them in particular rooms. The Aussie used to sneak up on the couch if left for very long with access to the living room--but the Dobes always told on him. The afghan removed one of the temperature control devices from an electric blanket--fortunately for him it was at the foot of the bed on my side and my husband gumpily repaired it--the bottom didn't heat but I was alway much too warm at the temperatures that he (my husband) liked so that worked out all right. Dogs that wouldn't think of looking in the trash if you were there who were prepared to spread it throughout the house if you weren't.
I mostly keep them crated if I'm not home to supervise--I do that for a long, long time. It's the old better safe than sorry business.
And I never, ever, ever leave two dogs loose in the same area--if one dog loose can get into trouble I guarantee you (from past experience) that two dogs can hit a geometric progression of trouble--gives the term "baddog" a brand new meaning.
Keep him crated awhile longer. 11 months is still pretty young--even though they aren't teething, young dogs do a thing that is called "setting" the teeth. It is accomplished by chewing on hard things--like the door frames, the deck, (or in the case of my youngest dog the fence itself--it now has some lovely new palings because of the fence chewing) the edges of the house--I've had several dogs do that until I figured out why they were being quiet and how they were entertaining themselves.