May there be a majority of a 503c Board members share an affliation with another 503c organization? Especially when it comes to holding executive positions in both, Treasurer for example.

Keep in mind that the legal form of the organization is not a "503c organization". Any charity or other entity eligible for tax exemption for it's donors pursuant to section 501 (c) of the Internal Revenue Code is an organization (typically a non-profit corporation) organized pursuant to state law.

But yes; there is seldom any provision of such state law prohibiting the officers or members of one such organization from also being officers or members of other such organizations. Why should there be? What is the problem in your case?

Yes in many religious corporations, it is common, since often a parent group will have two or three other groups under it but with separate corporation and tax exempt status. But many of the officers will be the same