You might be interested in hearing how I recently introduced a single hen to my flock of twenty.
Edith is a two-year old Buff Orpington whose flock was abandoned by the owner. I received word that this lonely hen was up for adoption after being brought to an animal shelter in another city. After they gave her a clean bill of health and wormed her, I brought her home just short of two weeks ago.
It's very touchy introducing one hen to a flock the size of mine. A smaller flock would be much easier since there are fewer personalities for the newcomer to learn to interact with. The normal reaction of any flock to a new hen is to let her know she isn't welcome, and that's exactly what happened. I had her in a large crate in the middle of the run, and they managed to bloody her comb through the wire sides. After I moved her to a safe pen, she fared much better.
After almost two weeks, Edith has bonded with me spectacularly, but she hasn't made any friends in the flock. In fact, they all appear to hate her, and several make a point of chasing her and delivering pecks to her rump every chance they get.
But in spite of that, Edith is learning which of the chickens are indifferent to her, rendering them fairly safe, and which ones she needs to watch out for. She developed strategies for avoiding conflicts, and one is to jump into my arms or onto my shoulder to escape a pursuer.
She has had very few problems roosting at night, and seems to be able to find a perch with little problem where she can roost in peace. In other words, she's adjusting rather well, and is becoming proficient in handling the pecking order.
We who have added or are thinking of adding, a single new hen to our flocks, need to accept that the adjustment is going to be very hard on the new hen, and it's not going to be possible for the flock to accept the newcomer instantly.
If possible, when thinking of adding a new hen, selecting a breed that is docile but not overly so will make it a little easier. If I had added a RIR or Barred Rock to my flock, there could have been a lot more conflict and fighting. Buffs are docile and generally accept things as they are and adapt without challenging the pecking order, therefore my flock dynamics haven't been greatly altered by this addition, making it much easier on everyone concerned.
As others have pointed out, interfering as little as possible during this merger will be best, just stepping in should the newcomer get outnumbered or overwhelmed. Edith lets me know when she requires my intervention, and most of the time, she does just fine adapting a little more each day to her new flock.