No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
If you have already exceeded your first 3 or so then there would most likely not be a bump in score for anymore being added but a ding, this ding can possibly be being overidden by your utilization rate dropping as each cards CL is added to overall util. Most dings to Fico for new accounts last up to 6 months and the points are recovered over that period of time. If your AAoA is already low there would not be a hit due to it falling even further.
It all depends on what's on your file. If you had a very thin file, then you would see a jump. If you had a decent file and the new accounts decreased your AAoA significantly, you'd see a bit of a drop. I don't worry about that, you need a good healthy thick file for your scores to grow. Congrats!