CBS' board of directors is set to discuss the fate of CEO Leslie Moonves on Monday following allegations of sexual misconduct that go as far back as the 1980s — but it's a complicated path to an ouster.

Moonves, 68, has been CEO at the broadcasting network for two decades and board chairman since 2003. The company has no written succession plan for Moonves in his capacity of chairman of the board, according to CBS' most recent annual report, which means a vote to remove him puts CBS on uncertain ground.

CBS shares were down nearly 4 percent Monday morning.

Moonves has been embroiled in a public dispute with principal owner National Amusements Inc., whose president, Shari Redstone, is on the CBS board.

Moonves has opposed efforts by Redstone to merge CBS with Viacom. NAI, also the principal shareholder of Viacom, had split the two companies into separate publicly traded corporations in late 2005.

In May, CBS filed a lawsuit against Redstone, her 95-year-old father, Sumner Redstone, and NAI alleging that NAI's proposed CBS-Viacom merger "is not in the best interests of CBS stockholders." The Redstone family later filed a complaint alleging that CBS had no legal right to strip them of voting privileges.

Sumner Redstone owns approximately 79.5 percent of the voting shares, and "there can be no assurance now or in the future that he or the successors to the voting control may not seek to effect succession of the Chairman," CBS said in its most recent annual report. "However, and in all cases, the Board will elect the next Chairman by a majority vote of the Board."