Plucking is rarely caused by just one thing. One thing can be what "triggers" it, but a parrot who plucks does so usually because a bunch of things have been going wrong and something pushes them over the edge.
A PARROT WHO STARTS PLUCKING NEEDS TO SEE A CERTIFIED AVAIN VET TO RULE OUT AN ILLNESS CAUSING THE PLUCKING!!!
A PARROT WHO STARTS PLUCKING IS NOT EXHIBITING "BAD BEHAVIOR" BUT A SERIOUS CRY FOR HELP!
Many of us here have birds who pluck, and many of us got those birds years after they started plucking and have not been able to get them to stop. I know I personally struggle to know if I have solved the issues that started the plucking, but 10 years after the problem started, solving the original issue may not help. Don't think of it as a behavior, think of it as a symptom. If you had a child who cried constantly it might SEEM like a behavior, but in reality a child who never stops crying dies so because he is absolutely miserable for some reason, and he PROBLEM needs to be fixed for the sake of the child. The crying itself is simply the child demonstrating his suffering.
After, and ONLY AFTER illness has been ruled out, the following issues should be looked into
Diet
Independent play skills (just because he has toys doesn't mean he knows how to play with them)
Anxiety related issues (could involve the new cage; changes like that are best made slowly)
Itchy skin
Infrequent bathing opportunities (your bird needs to bathe multiple times a week whether he likes it or not)
Not enough sunlight
Parasites
Something getting on his feathers and leaving a residue which bothers him
Not enough sleep
Boredom
Over production of breeding hormones (look at this article on hormone control
Handling Hormones ? Silver Sage Aviaries)
The list goes on and on.
The World Parrot Trust has a great pod cast on feather destructive behavior which you can listen to on their web page.