I used to do it with a bone - Bev started it there is vid on here somewhere. Nacho and Bev shared the bone. Taught him not to food guard "to share" - not suggesting you do this with two dogs sharing a bone together

that would be carnage!!
I used to start with low reward - like a ball - play pass the ball. In house - two dogs - one ball - let me use Nacho and BB as example.
Ball to Nacho - So I would look at BB and say not you good girl then pass ball to Nacho - good boy - said Give to Nacho got ball back - (they sitting or lying down in front of me - doesnt matter which as long as calm)
Then I would look at Nacho and say not you Nacho good boy then pass ball to BB - good girl - Give get ball back etc and so on
Eventually I could put ball in front of me and say Not You BB and say Nacho Ball and he would take ball and vice versa.
Takes a while but eventually you can use Not You for a lot of stuff - when you go to door when you are going out when they are demanding attention if you are on phone whatever.......
Then up the reward (ball was always high reward for Nach but to be honest was never mudge interested in anything else) Filled kong - 2 licks not letting go of kong to start with.
Not you BB - two licks Nacho - good boy good girl etc. Then I would put kong down ...... and so on.
Eventually I could do it with bowl of food or bone.... never a chicken wing though they did a quick disappearing act.

It may not be the best way of doing it but I never had any issues with it. To the point where if it was BB's ball - I could just say not you and Nacho wouldnt touch it. If out and there was a ball or a toy - not you - and neither would touch it.
I still use when going to work or leaving house or if I want couch to myself.