How to increase my vocal range?

I am a 15 year old male and I love singing and hope to someday pursue musical theatre (yes I spell it the British way). Right now, I'm trying to increase my vocal range because there are some notes I feel as if I can surely hit, but need the confidence and help to do it. My highest note comfortably is a G4 sometimes a A4 in falsetto. Recently I discovered that when I go up and down the scale I can sing an A4 perfectly when I'm just singing mi-mi-mi-mi-mi-mi-mi-mi-mi. I tried on other vowels but I couldn't seem to do it. I was wondering, what is the best way to increase my range? What is the proper breath support I'll need to get out these higher notes? Thanks in advanced for answering and also I have a vocal coach so I do also get outside help.