This site shows locations of the high order rainbows up to sixth order. My thought is that, There should be even higher order bows like 7th, 8th, etc. (Though they would be practically impossible to observe.)
So, Where would they appear on sky?
During rainbow events, both refraction & reflection occur in a raindrop. It should also be noted that reflection takes place at the inner side to a larger part. Hence, some of the incident light energy is indeed transmitted through the outer side of the drop. As reflections continue inside (as order increases), small amount of light is transmitted continuously through the other side, thereby making the bow fainter & fainter. Thus, further orders are very hard to notice. But, they still exist in theory & their location could be predicted theoretically.
Perhaps, this link is excellent regarding the calculation of higher orders. It also shows the location of higher-order bows for up to 12 - relative to the Sun-Earth system.