I've done this multiple times. I spend a lot of time at the beginning teaching the puppy manners. That means sit for toys, treat, meals, attention. It means leaving the other dog alone when they don't want to play. It means sharing my attention.
Toys are shared. There was no Moose-dog toy or Bat-dog toy. They belonged to both of them. At the same time, I made MY wanting their toy to be a bigger enticement than the other dog wanting their toy. I never let them take a toy from the other's immediate possession - that was immediately dealt with by refocusing the thief with a different toy and returning the stolen toy back to its appropriate dog. If the toy was not being played with, then it was free to whomever wanted it. I played "let me see it" with them. I would ask to see the toy and when the dog gave it to me, I would make big deal over the toy and when the dog sat, I would return the toy. I never gave the other dog the toy the first was actively playing with. This encouraged the dogs to want me to desire their toy rather than the other dog. All toys went into a "community chest" when playtime was done.
Treats and chews are given only when both dogs sit. And I am in the room with them. They are not allowed to take food from the other dog. That means treats, chews, or meals. Rather than simply separating them, I stayed with them and refocused all attempts at theft. It didn't take long for the dogs to learn that the other's food was not up for grabs. With Bat-dog, she was an inhaler while Moose-dog was a grazer. She learned very quickly that she was not to steal his food. At mealtimes, she would inhale her dinner, then sit politely while Moose-dog ate. Even if he walked away from his dish, she sat there. When I knew he was done, I would tell her OK and she would wipe his bowl clean. Sometimes he'd leave her a few kibbles. I really limited long lasting edibles and stuck with bisquits instead. With bite-size treats, I would have them sit and then give a treat to the first, then the second dog. Repeat as needed. This taught them that they would never be left out of the treat giving. For bisquits, I gave them at the same time and the slower eating dog took it and found a spot to enjoy it. The faster eater ate it in front of me and then I focused their attention on me until the other dog finished eating theirs
With Cat-dog and Tornado-dog, it's a bit different. She doesn't like toys, so there's no pushiness. With treats, she only eats them under the bed at night and in the morning. She doesn't care for chews. Mealtimes, they eat out of the same bowl. They both have the same eating intensity level and no aggression, so I have allowed it. I always fix two bowls, but they go back and forth between them together. I can give Tornado-dog long lasting chews because Cat-dog has no desire for them.
What I've done for obedience training has varied with each pairing.
With my Moose-dog (8 weeks old) and Dog (about 9 years), I just attached them with a double leash. Dog was very well-trained and her good behavior literally rubbed off on Moose-dog. When she sat, he sat; when she came, he came; when she stopped, he stopped. I never actually obedience trained him on his own because he picked it all up from her.
After Dog died, I brought home Bat-dog at 4 months. She was a bit more difficult due to her nose. And then she had a bad experience with a vet, so she developed people fears. With her, I enlisted the help of a friend. I walked and trained Bat-dog and she walked Moose-dog. He was thrilled because he loved her more than anyone. Moose-dog didn't need training, so my friend had no trouble handling him. Bat-dog was happy because she loved only me and I could put in the attention she needed for training. I used the double leash when we were alone. Whem my friend came, I said "take your dog" and gave her Moose-dog's leash. When Moose-dog got old and his back legs bothered him, I would hand her Bat-dog and they would explore while Moose-dog and I rested. Fortunately, by then Bat-dog had gotten over her grudge and had forgiven our friend.
With Cat-dog and Tornado-dog, I had a different challenge. Cat-dog has dog fear so I needed to work with her on that. Tornado-dog came at 7 weeks and is hyperactive. So again I enlisted my friend's help. I had her take Tornado-dog through an obedience class while I took Cat-dog. Now I use the double leash when alone and hand over "your dog" (Tornado-dog) to my friend when she's with us.