Once the dogs are interacting as closely as I can manage - and no one seems unhappy - I start arranging play dates. Now, play dates at my house are going to look different than play dates at your house. Mixing and matching seven dogs takes a bit of finesse, but many of the basic principles are the same across staycations.
Before I start introducing dogs without the aide of barriers, I make sure to set everyone up for success. If I'm concerned at all that dogs might not get along, I enlist an extra set of hands to help with the play date. I'll also have the dogs drag leashes so that if there is a fight, the dogs are easier to separate. I use our backyard for play dates as it's a larger space. This means the dogs have room to be as close or as far from each other as they would like. Last, I have a handful of treats available to distract or reward as needed (if the new dog has issues with food around other dogs, I will have picked up on it when I was passing treats out at the baby gate earlier).
I always introduce dogs to Piper Ann first. Of my dogs, she is the most chill. She's also the most responsive to my cues - if I ask her to come to me, she will drop whatever she's doing and come right away (mostly). Ideally, I want play dates to go the same way uncovering the baby gates did: a couple of friendly sniffs, and then move along, little doggies. Nothing to see here.
Of course, some times play happens on play dates. I don't stop play immediately, but I do watch very carefully to make sure it's healthy play. As I mentioned earlier, play is arousing, and it's easy for play-arousal to turn into fight-arousal. Unless the play I am observing is extremely comfortable and the dogs are playing like long lost friends (this has never happened to me in approximately a billion years of fostering), I interrupt play every ten to fifteen seconds by passing out treats.
What does healthy play look like?
This is going to take longer than a paragraph to answer. There are actually hours long seminars and lectures on the topic. But there are a few things I look for. Is the play equal? Are both dogs having fun? Dogs who are strangers will trade rolls. For example, if they are wrestling, they should be sharing time as the dog jumping on top of the other and the dog closer to the ground. I also watch for calming signals. Good play should have calming signals, and the dogs should mirror each other's signals. So if one dog stops to sniff, the other should stop to sniff as well. For play to be healthy, the dogs should naturally interrupt themselves, just a few seconds every fifteen seconds or so. If the dogs aren't interrupting themselves, then I definitely need to step in.
Frequent interrupting helps keep arousal levels low and under control. The longer dogs play without interrupting, the higher the risk of play turning into a dog fight. If dogs are just chilling in the same yard, the first play date will last about twenty minutes. If dogs are playing, I'll stop the date after about ten minutes - less than that for intense play. If the first play date goes well, I will start gradually increasing the amount of time dogs spend together. However, I will always error on the side of keeping things sort and sweet. A dog fight at this point can be disastrous, and you may end up spending months repairing a bad first impression.
At the risk of sounding redundant: you have nothing to lose by going slowly. You have everything to lose by moving too quickly.