As a Monday deadline neared for the Bancroft family to decide on Rupert Murdoch's $5 billion offer for Dow Jones & Co., last-minute wrangling by family members and their trustees intensified.

Family lawyers were scrambling Friday to change the voting structure of the biggest Bancroft trust so it would better reflect the views of all the beneficiaries. The trust's overseers include Christopher Bancroft, a prominent family member who has been outspoken in his opposition to the deal. The restructuring could dilute Mr. Bancroft's...