As a new user, the maximum is two. We get a lot of new users, over at Game Dev, performing the actions mentioned by NVZ after the first two images.
As per users with over 10 reputation, let's see:
I am going to go with far more than I have time to test; but most importantly, far more than you should ever need.
As per needing to upload more than your allowed; once again, you should not really need to. An image can be compounded. If you need to upload three images, but are only restricted to two, use some simple image processing software like paint to make a larger image out of the two. You can label them as "figures" or "diagrams", and refer to them from your question as "as you can see, in figure one..". Technically, your not actually circumnavigating the system, and your not relying on another user to fix it.