  Since low-mass stars have low luminosities, orbits at which liquid water can
exist on Earth-sized planets are relatively close-in, which produces Doppler
signals that are detectable using state-of-the-art Doppler spectroscopy. GJ
667C is already known to be orbited by two super-Earth candidates. We
investigate whether the data supports the presence of additional companions. We
obtain new Doppler measurements from HARPS extracted spectra and combined them
with those obtained from the PFS and HIRES spectrographs. We used Bayesian and
periodogram-based methods to re-assess the number of candidates and evaluated
the confidence of each detection. Among other tests, we validated the planet
candidates by analyzing correlations of each Doppler signal activity indices
and investigate quasi-periodicity. Doppler measurements of GJ 667C are
described better by six Keplerian-like signals: the two known candidates (b and
c); three additional few-Earth mass candidates with periods of 92, 62 and 39
days (d, e and f); a cold super-Earth in a 260-day orbit (g) and tantalizing
evidence of a $\sim$ 1 M$_\oplus$ object in a close-in orbit of 17 days (h). We
explore whether long-term stable orbits are compatible with the data by
integrating 8$\times 10^4$ solutions derived from the Bayesian samplings. The
system consisting of six planets is compatible with dynamically stable
configurations. As for the solar system, the most stable solutions do not
contain mean-motion resonances and are described well by analytic
Laplace-Lagrange solutions. The presence of a seventh planet (h) is supported
by the fact that it appears squarely centered on the only island of stability
left in the six-planet solution. Habitability assessments accounting for the
stellar flux, as well as tidal dissipation effects, indicate that three (maybe
four) planets are potentially habitable...
