Introducing New Rats to 1 1/2 year old Rat

Question
QUESTION: I have a 1 1/2 year old female Black Berkshire rat named Berkley.  She's adorable!!  I've had her since she was about six weeks old.  
I recently adopted/rescued two female rats from the animal shelter who are approximately six months old.  I have had the new rats about five weeks.

My question is about the best way to introduce them.
When is it the right time to allow them to have full access to each other?  I don't want them to get hurt.

Here's what I've been doing:
first day I held each new rat up to Berkley's cage one-at-a-time so she could see what she was smelling.  She knew they were there after just a few minutes of them arriving.  She's so smart!
I put them in a separate cage and kept them away from Berkley for a week just to observe them and make sure there were no obvious illnesses or issues.  The next week I put their cages next to each other but far enough away that they couldn't actually touch each other.   Once they started to get used to each other I began moving their cages closer (a couple of centimeters apart) for an hour or so a day, gradually longer.  
  Next I started letting them play together with the new rats in the balls and Berkley roaming free.  I was careful not to allow the ball to scare Berkley or run in to her.  They were doing a lot of licking and smelling; no signs of aggression.  
  Then I reversed this... Berkley in the ball and the others roaming free.

They all seem to like each other.  Lots of smelling, licking and trying to touch each other.  

So, I moved their cages close together - touching.  All went well for several hours until evening.  I was in the same room with them all afternoon and evening until I started getting ready for bed.  I heard one rat making distress sounds and it's right front paw had one "finger" with a little blood on it. I'm not sure what happened and it didn't seem to be in pain.  I held a tissue against it until it stopped bleeding (a few seconds).  So, I separated the cages and put the new rats on the other side of the room for the rest of the night so they could calm down and rest.

Tried it again... gradually getting the cages closer together, standing by talking to them to see how it would go.  They seem to be getting along well and then I hear another distress sound and the same new rat is bleeding from both front feet and what looked like teeth marks. I don't know if Berkley bit her or if her cagemate bit her.  I have observed that she is annoying to her cagemate occasionally.

I am wondering if this rat is too "playfully aggressive" for Berkley.  Is Berkley too old to introduce her to the new rats?

I attempted this again and it's going well.  The cages are not touching but are close.  And the rats still play together where either Berkley or the new rats are in exercise balls and the other are roaming free.   

I am afraid to put them together and give them full access to one another.  
Please help me determine if they will get along well or not.

I am not sure if the previous injuries were from Berkley or the other new rat.  The one who has been injured  IS  slightly forceful with her grooming of the other new rat.  I am not sure how Berkley will react to this.

Please feel free to tell me anything you think will help.  I appreciate your advice and assistance in this matter.

I want Berkley to have friends but I don't want any of them to get hurt!!  AT  ALL!!!

Thank You!!!!

ANSWER: Hey Carolyn!
First I would suggest learning the signs of dominance. (I can help you on that!)
Here are some of the tell-tale signs of a rat being or trying to be an alpha:
Normally power grooming (Pretty advanced grooming)pushing down and tackling are signs of dominance.

I would use the switch cage method with your case.
Here is how you do it:
Have two cages and keep both rats in it for a week.
Then after the week switch the rats after the week with out cleaning the cage.
Repeat.

Since your rats seem to be able to play together this is mostly seeing who's boss,
because your rats are older fighting might always happen every once in a while.
Continue what you are doing for the most part, and eventually they will get to know each other and like each other more.
Good Luck!
Emma
Don't hesitate to ask any more questions!

---------- FOLLOW-UP ----------

QUESTION: Thank you.  I'll continue being Patient with this process and do a cage-switch rotation again.  

Should I seperate the two new ones from each other at all?!  Not sure it would help the process but it often seems like the darker new one (the less dominant one) and my older one get along better.   ...just wondering...?

Answer
Hi,
Sorry it took so long!
This is what I would do:
1. Separate the two new ones and do the cage rotation thing.
2. Continue having them play together under supervision
Do both of those and, yes, continue to be patient.
Hope this helped!
Emma