DETROIT — General Motors and Tesla are automakers of different vintages but increasingly mutual aspirations. They found another bit of common ground on Tuesday as both beat back proposals from dissident investors to shake up their ways of doing business.

For General Motors, it was a bid to replace three company directors and split the automaker’s stock into two classes. For Tesla, the electric-car upstart, it was an initiative to impose one-year terms on board members to create more independence from the company’s chairman and chief executive, Elon Musk.

The proposals at G.M., by the hedge fund Greenlight Capital, which owns a 3.6 percent stake in the company, were aimed at bolstering the sagging value of the automaker’s stock.

G.M.’s chief executive, Mary T. Barra, and its board opposed the moves, which would have included creating two classes of stock — one paying a dividend and a second tracking earnings growth.