Having several close friends simultaniously can be very rewarding and enriching.
In my own past, I was much like you -- generally only having one or maybe two people around I'm close with/to. Part of that is probably related to my Myers-Briggs/Keirsey temperament (INFP -- introversion), but part of it relates to childhood abuse and neglect, which made me somewhat socially withdrawn in my young days. Gradually, I'm becoming more of an "ambivert" (google it).
Allowing yourself to unfold and change can bring color and depth and zing to your life. Don't cling to who you think you are, but let yourself become what you are becoming. I'd say. Accept the challenges of allowing more people get close to you, and I think you will not regret it.