The only way you can have too much tea is if it starts flowing out your eyes while you're drinking your newest cup.
Personally, I drink nothing but tea. Really. The last time I drank anything else was over a week ago, and only because movie theaters don't serve tea, so I had bottled water instead. I go through about 2 quarts of iced tea a day by myself (more if I exercise), plus whatever hot tea I consume. That's how I've lived for 7 years now. Back in high school I started drinking tea because I was getting sick of buying a liter of Dr. Pepper every morning, so I brought a liter of tea with me every day. After about a month and a half, I found out I didn't enjoy soda anymore. It tasted too sweet, too syrupy, and didn't actually relieve thirst. Since then, I've drank almost nothing but tea. Literally. If I can't get tea, I literally won't drink anything. To the point of not drinking anything for upwards of 16 hours straight. My friends in high school (and my friends now) swear up and down that if you cut me, I'll bleed tea instead of blood.
I am perfectly healthy (aside from vicious allergies, which I find alleviated by a good cup of Assam or Yunnan Gold) and I have no difficulty sleeping. I would dare to wager that I am far healthier for all my tea drinking than I would be if I were still drinking Dr. Pepper every morning (and I'm sure my teeth are much happier, too).
You can only be drinking too much tea when it starts flowing out your eyes as you drink more.