It means this relatively nearby star, Gliese 667C, now has three so-called super-Earths orbiting in its "habitable zone".
This is the region where temperatures ought to allow for the possibility of liquid water, although no-one can say for sure what conditions are really like on these planets.
Gliese 667C is 22 light-years away.
Astronomers can see it on the sky in the constellation of Scorpius (The Scorpion).
Previous studies of Gliese 667C had established there were very likely three planets around it, with its habitable zone occupied by one super-Earth - an object slightly bigger than our home world, but probably still with a rocky surface.
Now, a team of astronomers led by Guillem Anglada-Escude of the University of GÃ¶ttingen, Germany, and Mikko Tuomi, of the University of Hertfordshire, UK, has re-examined the system and raised the star's complement of planets.
The researchers used a suite of telescopes including the 3.6m telescope at the Silla Observatory in Chile.  This incorporates the high-precision Harps instrument. Harps employs an indirect method of detection that infers the existence of orbiting planets from the way their gravity makes a parent star appear to twitch in its motion across the sky.
The planets' presence needs to be disentangled from this complex signal but the Harps instrument is recognised as having tremendous success in identifying smaller worlds.
Gliese 667C is a low-luminosity "M-dwarf" star just over one-third the mass of our Sun.
This means its habitable zone can be much closer in before temperatures make liquid water impossible.  The team is now confident that three rocky worlds occupy this region at Gilese 667C.
"Their estimated masses range from 2.7 to 3.8 that of the Earth's," Mikko Tuomi told BBC News.
"However, we can only estimate the physical sizes by assuming certain compositions that is, well, only educated guessing.
"Their orbital periods are 28, 39, and 62 days, which means that they all orbit the star closer to its surface than Mercury in our own system. Yet, the estimated surface temperatures enable the existence of liquid water on them because of the low luminosity and low mass of the star."
These planets are said to completely fill the habitable zone.  There are no more stable orbits in which to fit another planet.
That said, the team has found tantalising evidence for what may be another rocky world on the inner-edge of the zone. This would be a seventh planet in the system.
The planets would need an atmosphere to sustain liquid water on their surfaces, but at a distance of more than 200 trillion km, there are no means currently to determine what the precise conditions are like or whether life would have any chance of establishing itself.
Nonetheless, Dr Tuomi believes M-dwarf stars are good candidates to go hunting for potentially habitable worlds.
They are small enough that close-in rocky planets will show up well in the Harps Doppler spectroscopy data, but they are also dim enough that those close-orbiting worlds will not be roasted.
"This discovery single-handedly demonstrates that low-mass stars can be hosts of several potentially habitable planets," explained Dr Tuomi.
"In practice, it means that we might have to double or treble our estimates for the occurrence rate of habitable-zone planets around M-dwarf stars.
"There might, in fact, be more habitable-zone planets in the Universe than there are stars, which makes it much easier for the future space missions to obtain images of these planets.
"So, although only a rather simple discovery, its implications might force us to re-think how common habitable-zone planets are in the Universe."
The research has been written up for the journal Astronomy & Astrophysics.
Jonathan.Amos-INTERNET@bbc.co.uk and follow me on Twitter: @BBCAmos
Scientists have identified three new planets around a star they already suspected of hosting a trio of worlds.