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We extend the source sample recently observed by the Breakthrough Listen Initiative by including additional stars (with parallaxes measured by Gaia) that also reside within the FWHM of the GBT and Parkes radio telescope target fields. These stars have estimated distances as listed in the extensions of the Gaia DR2 catalogue. Enlarging the sample from 1327 to 288315 stellar objects permits us to achieve substantially better Continuous Waveform Transmitter Rate Figures of Merit (CWTFM) than any previous analysis, and allows us to place the tightest limits yet on the prevalence of nearby high-duty-cycle extraterrestrial transmitters. The results suggest $\lesssim 0.0660^{+0.0004}_{-0.0003}$% of stellar systems within 50 pc host such transmitters (assuming an EIRP $ \gtrsim 10^{13}$ W) and $\lesssim 0.039^{+0.004}_{-0.008}$% within 200 pc (assuming an EIRP $\gtrsim 2.5 \times 10^{14}$ W). We further extend our analysis to much greater distances, though we caution that the detection of narrow-band signals beyond a few hundred pc may be affected by interstellar scintillation. The extended sample also permits us to place new constraints on the prevalence of extraterrestrial transmitters by stellar type and spectral class. Our results suggest targeted analyses of SETI radio data can benefit from taking into account the fact that in addition to the target at the field centre, many other cosmic objects reside within the primary beam response of a parabolic radio telescope. These include foreground and background galactic stars, but also extragalactic systems. With distances measured by Gaia, these additional sources can be used to place improved limits on the prevalence of extraterrestrial transmitters, and extend the analysis to a wide range of cosmic objects.