MOUNTAIN VIEW, Calif. — The little spacecraft that could may still have some life left in it.

Hearts were broken around the lonely cosmos in the spring when a critical wheel on NASA’s Kepler spacecraft got stuck, leaving its telescope unable to point precisely enough to continue prospecting for Earthlike planets in a starry patch of the Milky Way. But Kepler’s managers say they have a plan that could keep it hunting for these exoplanets for three or four more years.

“K2: The story begins,” Steve Howell, Kepler’s project scientist, told a recent gathering of astronomers here at NASA’s Ames Research Center, borrowing the name of the world’s second-highest mountain to herald the proposed mission.

In its four years of monitoring the brightness of each of 160,000 stars in one patch of sky, Kepler identified 3,500 possible exoplanets by seeing stars dim when planets crossed in front of them. It also enabled the first rough estimate of the abundance of habitable planets in the Milky Way: about one in five sunlike stars have potentially habitable Earth-size planets, meaning billions of chances for the existence of E.T. Not to mention how it revolutionized the understanding of the internal structures of the stars themselves through the practice of “asteroseismology.”

But the little spacecraft was only beginning to zero in on planets with orbits analogous to our own, Earth-size worlds that take a year to orbit suns similar to our own, candidates for Earth 2.0, in the vernacular. K2 would no longer train Kepler on only one set of stars. Instead, it would skip around the sky, monitoring the stars in one spot continuously for up to 80 days.