The star HD 40307 was known to host three planets, all of them too near to support liquid water.
But research to appear in Astronomy and Astrophysics has found three more - among them a "super-Earth" seven times our planet's mass, in the habitable zone where liquid water can exist.
Many more observations will be needed to confirm any other similarities.
But the find joins an ever-larger catalogue of more than 800 known exoplanets, and it seems only a matter of time before astronomers spot an "Earth 2.0" - a rocky planet with an atmosphere circling a Sun-like star in the habitable zone.
HD 40307, which lies 42 light-years away, is not particularly Sun-like - it is a smaller, cooler version of our star emitting orange light.