I have heard lots of people say that two puffers should not be put together, although I do see some together in fish stores. That being said, it is also true that pet stores don't have much, if any - decorations in the tank where the fish can become terratorial.
I also think it depend on tank size, swimming room and personality of the current puffer. Is he an easy going guy or what? Has he been with other fish, if so - how did deal with that and what kind was he with. How long do you have your current puffer. I think if they are young, they can adapt assuming they have sufficient swimming room.
As they get older, just like people - I think their tollerence for new inhabitants, especially a young fish that can become agressive will not be a welcome guest in his tank.
I have a dog face puffer and he is such a sweety and gentleman. I have put ghost shrimp in there as a treat - he hasn't eaten them. He does not eat typical things that most people say that their puffer will eat. My little guy is not the norm I guess. Because of his easy going nature, I have thought about adding a puffer as a tank mate to his 90 gallon tank - any my puffer is in there buy himself right now and he is about 5 inches. I know I will need a bigger tank someday because he will grow big and will need the space, a nice 180 or 225 sounds good
But until then, I think since there is doubt out there, I wouldn't suggest it. Puffers seem to do well with tangs or some of the fish in the wrasse family - such as the Australian caught Tusk fish. We had one for a short while and our puffer loved him. We will probably get one again someday.
Foxface fish are cool.
I am not knowledgable about the puffer species that you have and don't know how big they grow. But, my bid is to not chance getting a second puffer.