This plugin is designed with size / load time in mind and specifically promoted for those qualities. The more that is pulled, the more time it will take for your page to load. It was decided that 10 was a good limit for these reasons.
However, we had received a logical argument for increasing the limit at least to 12 – because with 12, there are more block-tiling options, like 2×6, 6×2, 3×4, 4×3, rather than just 5×2/2×5.
It is likely that you will see an increase to a limit of 12 per display in near future versions.
What you can do is feed multiple displays, like using two or three widgets, or using multiple Easy Instagram shortcodes on one page/post. I like to (for instance) feature 4 images from each of 4 hashed tags on one full-screen layout page, side by side, so that I’ve got a 4×4 gallery featuring four tags for a total of sixteen images on the page.