New Delhi, Sept. 19 -- Shortly before noon on Sept. 17, the directors of Tata Sons Pvt., Ltd. the holding company for India's biggest conglomerate, gathered in a sleek boardroom on the fourth floor of its headquarters for a meeting.

On one side of the long table that can accommodate 20 people sat Noel Tata, chairman of Tata Trusts, the group of charities that own 66% of the holding company that in turn controls some of India's biggest brand names from Air India to Jaguar Land Rover. Sleeves rolled up, a seven-page document at the ready, he came prepared with a strategy to keep the company that carries his family name in private hands.

Among those facing him was Natarajan Chandrasekaran, chairman of Tata Sons, wearing a suit and a fuchsi...