I know some will disagree with what I am about to say. This is just my experience and not necessarily representative of how everyone's schoutedenis act together.
This is a tough question and one I was asking myself a lot in April. I had one adult schoutedeni who I had grown from a juvenile and was contemplating getting her a companion, especially after what I had read on this forum about some others' experiences with schoutedenis seeming to do very well in groups. My agonizing over what to do was "solved" when my spouse got me a baby schoutedeni for my birthday, and the only place for him to go was in her tank. It did not go well at all. The male baby was very friendly, and the adult female wanted absolutely nothing to do with him. The female, who is my pride and joy and used to get so excited when I came home, a very friendly, happy puffer, became withdrawn and was always hiding from the male baby. It got to the point where the adult female began choosing hiding from him over eating, and that was when I got another tank for him. (The one upshot to the story is that I was able to definitively determine their genders based on the male's incessant attempted practice mating advances toward the adult female.) Even with moving him, it still took a few months for the adult female to start to come out of her shell again.
Since I was going to be moving him into a new habitat, and I wanted more schoutedenis, I decided to get a 125g tank and purchased 5 more schoutedenis, for a total of 6 in the 125g. I introduced them all at the same time, which I think is a key thing from what I have observed, because their territories haven't already been established. That, and they are all about the same age, not one adult and one baby. If you did decide to purchase more, I know it sounds drastic, but if it were me, I would move them all into a new tank at the same time, as I think that would help cut down on the aggression. Getting them around the same age will help, too. It's absolutely terrifying to watch a full grown puffer go after a baby puffer, even if it's only a pseudo-nipping territory spat. I would also make the tank MUCH bigger than you thought necessary. Another thing I have learned from watching the 125g closely is that these puffers seem to require A LOT more territory per puffer than I had anticipated, particularly as they are still babies. I am not sure that the 125g is going to be big enough for all 6 of them territory-wise when they are grown. At that point, I may have to get another 55g or a 75g for 2 of them and transfer them to the tank simultaneously, as well (and hope my spouse doesn't leave me. He already thinks I am nutso for the tanks I have
). This is not a function of my 125g not being properly aquascaped, either, as the tank is a veritable warren of rocks, wood, and plants. I observed the puffers and then re-scaped the tank, taking great pains to break up lines of sight with rocks, wood, and plants, after being able to see specifically how they behave and interact. There are very few territory spats now, but they are still very young. It's also much harder in a group this size to feed any "underdog" schoutedeni that you might get if the ones you get are much smaller than your current schoutedeni and/or more aggressive. It's taking A LOT of work to keep one of the 6 in the 125 with even a tiny convex belly, and they are all about the same age/size. The rest are complete gorgers, but this one is very shy and defers to the others on food every time, so I have to sneak him/her food when the others can't see (another advantage of the many breaks in lines of sight.)
I hope some of this helps. Again, it's just been my experience and I'm sure not indicative of how this goes every time for everyone. It may be that I just happened to get a batch of puffers with these particular personalities!
They are as spoilt as I let them and they love exploring new things. 
