There seems to be a relatively rarely used grammatical pattern consisting of either a single か clause, or a AかBか, or else Aかどうか, followed by にもよりません。
Based on the scanty examples of this that can be found online, it seems to mean something like "irrespective of". Aかにもよりません seems to mean that it isn't a problem if the question posed by A doesn't have an affirmative answer: "regardless of whether A". Similarly, AかBかにもよりません seems to mean "regardless of whether A or B".
But really, what is the meaning? Plus other considerations like usage restrictions and whatnot.