Welcome to the board! Glad to hear it's been a huge help for you. I know we'd all be interested in seeing pictures if you wanted to post some. Sounds like a great tank.
I don't have experience with sororities, but saw no one responded so wanted to throw in a quick word.
I know you didn't suggest this in your post, but goldfish are not good tank mates for bettas. They require a very large amount of space per fish, and also much cooler water than what bettas prefer. However, I, like you, have a soft spot for them. Not sure why... but eventually I would love a tank for some oranda's or possibly pearlscale. But then part of me wonders if I really want to bring a goldfish indoors when they are doing so well in my outdoor pond?
I'm rambling... I would say yes, you can add a school of another fish. I'm not very familiar with all species of tetras, but I think cherry barbs may be a little aggressive (or is it tiger barbs?). I would choose a peaceful fish to add to the group. Also, tetras are a toss up on whether they will be nippy or not. Some users swear that tetras are safe, others will say the exact opposite. Regardless it is important to have a proper school so aggression is spread out. Some options may be harlequin rasboras, platies, corydoras (which i personally love), shrimp (more the merrier, but they may become snacks). There are more options, but these are the ones that come to the top of my head.
The important thing is not to add too many fish at once. Not sure how established your tank is, but let it settle and adjust to the 4 new girls, then after a few weeks look into adding other fish.
Hopefully some users with more sorority experience will post soon. But hope this gets you started!