I did this the other day it was tailored to that persons situation but the basics are there for meeting and integrating in the early days so should be some help generally.
As a 13month entire male he isnt going to have a puppy licence and is a young adult. Your doing the right thing letting them meet and play on neutral territory, but home turf can sometimes be a different thing. Ive had 3 adult females at one time introduced at various times, ages 4, 5 then a 15mth old.
The first two were already spayed before I got them from the rescue, the youngest wasnt so a simlar sort of situation although dont know if your other two are neutered or not? So could be a little more tricky if they are not and he is as well.
If dogs are ging to kick off and compete then the usual main triggers are, Food, toys, treats like chews, attention, confined spaces and times of hyper excitement like leads coming out for walks, visitors coming, and door bells ringing. So what i do when introducing and integrating them is to be wary of these triggers that can set them off and deal with them accordingly. When you bring a new dog in, often you dont also see their full personalities emerging until at least probably 2/3 weeks down the line sometimes even more, so those first few weeks especially you need to be careful, being over causious is better then being under at least until you know whats what and get them intergrated and fully accepted. Bringing a pup in is different to a sexually mature adolsecent or young adult, Older dogs tend to accept more from a pup in the main and wont accept so much off an older dog.
I always give them there forever place to eat as soon as they arrive. If you have baby gates then use those to separate them, give them a wide margin of space to eat, supervise and dont allow eyeing up each others bowls, approaching each others bowls even when empty, bowls up and gone before allowing them free access to each other as well. Be careful of dropped food, animal or human when they are all together, both going for a piece of dropped food can set off a squabble.
With toys, chews and treats, dont leave them lying about for the same reason, if you are giving them supervised only, make sure everyone has a wide margin of space, and again remove them when unattended or when they all start to lose interest.
Vying for attention can also cause squabbles with some dogs, so dont overfuss them especially the new one when the others are present.
Also watch them in confined spaces, like all trying to get out of a door together, narrow halls of places where they have to jump over each other or pass close too, that can set some dogs off, so just be aware of those situations.
Times of hyper excitement too like door bells ringing, visitors coming an leads coming out for walks, can hyper some dogs up, and in a heightened aroused state, grumbling and shoving can sometimes set off a squabble.
As said a lot may well be over cautious and may not be needed but it should avoid any possible problems that may set them off. A lot depends on the individual dogs and personalities and depending on what you have already and what he is like he could fit straight in its possible. But doesnt hurt.
