WASHINGTON—Johnson & Johnson is asking for Supreme Court review of a $2 billion verdict in favor of women who claim they developed ovarian cancer from using the company’s talc products. The case features an array of high-profile attorneys, some in unusual alliances, including former independent counsel Kenneth Starr, who is representing the women who sued Johnson & Johnson. The nation’s largest business groups are backing the company, and a justice’s father also makes an appearance because of his long association with the trade group for cosmetics and personal care products. The court could say as soon as Tuesday whether it will get involved. At the root, Johnson & Johnson argues that the company didn’t get a fair shake in a trial in state court in Missouri that resulted in an initial $4.7 billion verdict in favor of 22 women who used talc products and developed ovarian cancer. A state appeals …