  GJ1132 is a nearby red dwarf known to host a transiting Earth-size planet.
After its initial detection, we pursued an intense follow-up with the HARPS
velocimeter. We now confirm the detection of GJ1132b with radial velocities
only. We refined its orbital parameters and, in particular, its mass ($m_b =
1.66\pm0.23 M_\oplus$), density ($\rho_b = 6.3\pm1.3$ g.cm$^{-3}$) and
eccentricity ($e_b < 0.22 $; 95\%). We also detect at least one more planet in
the system. GJ1132c is a super-Earth with period $P_c = 8.93\pm0.01$ days and
minimum mass $m_c \sin i_c = 2.64\pm0.44~M_\oplus$. Receiving about 1.9 times
more flux than Earth in our solar system, its equilibrium temperature is that
of a temperate planet ($T_{eq}=230-300$ K for albedos $A=0.75-0.00$) and places
GJ1132c near the inner edge of the so-called habitable zone. Despite an a
priori favourable orientation for the system, $Spitzer$ observations reject
most transit configurations, leaving a posterior probability $<1\%$ that
GJ1132c transits. GJ1132(d) is a third signal with period $P_d = 177\pm5$ days
attributed to either a planet candidate with minimum mass $m_d \sin i_d =
8.4^{+1.7}_{-2.5}~M_\oplus$ or stellar activity. (abridged)
