2 BTs, not boxers...same issues
I don't have 2 boxers; that would be my daughter who just adopted her 2nd. But my 2 bostons have the same problem. Lulu, the younger one, always, ALWAYS has to have whatever Sadie has and Sadie is really good about just giving it up. But if Lulu has something Sadie wants, Sadie just picks up any old toy and of course Lulu drops whatever she has and runs over to take from Sadie...then Sadie does a mad dash and grabs what Lulu dropped! Pretty smart, my Sadie is! Then Lulu gets all pouty and just lies on the rug like she doesn't have 50 other things to chew on/play with.
Many times Lulu, with a toy on tow, will smash into Sadie, letting her know it's time for a tug-of-war! Of course Lulu always wins (Sadie such a softy) but they have a ball together with much grunting and growling.
I think Bostons are really miniature versions of boxers!