This is currently being discussed on the X-Wing Reddit sub.
Read the card texts for Accuracy Corrector and R7-T1. They both contain two sets of "may" abilities. Then read the FAQ entry for R7-T1.
It seems pretty clear to me that, for 3 points, Accuracy Corrector's second "may" is only possible if you chose to cancel the dice results using the first "may", but that's inconsistent with the similar phrasing and ruling for R7-T1.
We probably won't get a clarification on this until Wave VI is released, but I'm finding it tough to come up with an argument why AC should not work like R7-T1 until then.
Are there other examples of cards with two sets of "may" abilities?
Edited by DagobahDave