Firstly, rest assured I'm investigating all performance issues being reported, like the one by Ami. As stated elsewhere I've already made a lot of improvements for 1.8, and will be adding caching on top of that shortly. Surprisingly, the biggest bottlenecks in my testing were not SQL queries. Two are described here, you could try implementing those.
Regarding plugins, there's not a whole lot that Q2A can do if they are slow. Adding more and more plugins is generally going to mean adding more and more code and often more SQL queries.
If you're able to diagnose any specific problems such as slow queries or inefficient code in plugins, do let me know and I'll see if I can suggest improvements.
Finally, 1.5 million page views a day is HUGE so you should have good hosting to match. This isn't limited to Q2A, if you had that many page views on Wordpress or Joomla (or any PHP app) without any caching, you'd also have problems. It sounds like you do have good hosting though.
BTW if you're not using PHP 5.6 it's worth upgrading to that, or even PHP 7 if possible.