As usual I am giving way too much detail in this post (it helps me think to write it out LOL) so feel free to skip to the last paragraph for the actual questions.
Also, this isn't something that I'm actually worried about in terms of aggression or anything
--if Abi picks up a toy Hector's not playing with he doesn't care, and they're not actually fighting or squabbling at all. It's just because I think they might enjoy their play better if he's not so worried about protecting his toys. Just to be clear.
Basically, once Hector gets a toy, he's naturally prone to being very possessive over it. When I first got him, if you gave him a toy, he'd run and hide it immediately, and if you didn't let him, he'd refuse to let go no matter what. It took a lot of work but I got him over that, and now he not only drops his toys nicely on command and even plays fetch (though he definitely doesn't care for it so we don't do it often--he likes going after the toy, but the retrieve isn't so fun for him), he often initiates tug with me by offering me his toy and things like that. He loves playing tug and chase with both people and dogs.
Abi, my new puppy, is also toy crazy and they love to play together. They usually play chase, with Hector carrying his toy and Abi chasing him. Sometimes she manages to grab it in a sneak attack (she's a lot more agile than he is, so he'll lose some speed on a corner or something and she'll manage to grab it) and they play tug, and he loves it! He gets really into it even though he's basically just dragging her around since he has like 40 pounds on her. LOL
What prompted me to write this though is that I think he's sometimes shutting down play sessions that he'd actually like to have. If he's chewing on or sleeping with a toy (which is most of the time), Abi will usually initiate by darting up like she's going to grab the toy. Hector responds by grumping at her quite seriously (not one of his "play with me" noises) while excitedly jumping up, turning his back and laying back down, then holding his toy. Abi will sometimes find another way to get his attention (such as sitting on him LOL), and he'll respond enthusiastically. Often she gets discouraged and walks away though, to which Hector responds by looking at her, groaning pathetically and sighing, which is his standard "why won't you play with me" reaction (I've seen it often because he regularly tries to initiate play with my older dogs, who get tired of it quickly due to age and shut him down). I mean maybe I'm reading too much into it, but I've also seen him legitimately not want to play with her and his response is different (no groaning or watching her, and generally he actually stands up fully and walks away rather than flipping around quickly).
I think they might enjoy their play more if he learns to be less possessive about his toys, because then they could tug more, and he wouldn't be accidentally discouraging her from playing with him.
I know how to teach dogs to play nicely if they don't know (like the ones who get overexcited and turn play into squabbles, that sort of thing), and I know how to teach dogs to get over their toy possessiveness with people, but I don't really know how to put it together, or if I should. I'm kind of new to the whole "dogs who like toys for toys' sake" thing as my older dogs only ever play socially with me, and don't actually care about the toy itself (case in point, I was just playing tug with Bandit, and Abi came up and wanted to tug with him, so I handed her my end of the rope...and Bandit immediately dropped his end and came back to play with me LOL).
So, after probably way too many words, back to my question: is this something you'd try to work on with your dogs, and if so, how would you do it? How possible is it to change how dogs play together? I put this in General Behavior rather than the how-to section as I'm also just kind of interested in what people think about interfering with dog play as long as everything is safe and fun for the dogs involved.