I feel like both "may not" and "not necessarily" contain the idea of possibility. Therefore, I find "may not necessarily" somewhat redundant. I would like to know whether "may not" can always be replaced by "do(es) not" or is/are/am not" when it is used in conjunction with "not necessarily".
In other words, is there a difference/a correct version in these 2 example sentences when using "are" and "does" instead of "may (be)"?
1) Boosted bee populations in organic farms may/are not necessarily (be) due to reduced pesticide amounts. In fact, in some instances the risk of intoxication may even be higher in organic farmland.
2) Having cancer does/may not necessarily mean that you will die soon.