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We present LMT/AzTEC 1.1mm observations of $\sim100$ luminous high-redshiftdusty star-forming galaxy candidates from the $\sim600\,$sq.deg$Herschel$-ATLAS survey, selected on the basis of their SPIRE red far-infraredcolours and with $S_{500\mu\rm m}=35-80$ mJy. With an effective $\theta_{\rmFWHM}\approx9.5\,$ arcsec angular resolution, our observations reveal that atleast 9 per cent of the targets break into multiple systems with SNR $\geq 4$members. The fraction of multiple systems increases to $\sim23\,$ per cent (ormore) if some non-detected targets are considered multiples, as suggested bythe data. Combining the new AzTEC and deblended $Herschel$ photometry we derivephotometric redshifts, IR luminosities, and star formation rates. While themedian redshifts of the multiple and single systems are similar $(z_{\rmmed}\approx3.6)$, the redshift distribution of the latter is skewed towardshigher redshifts. Of the AzTEC sources $\sim85\,$ per cent lie at $z_{\rmphot}>3$ while $\sim33\,$ per cent are at $z_{\rm phot}>4$. This corresponds toa lower limit on the space density of ultra-red sources at $4<z<6$ of$\sim3\times10^{-7}\, \textrm{Mpc}^{-3}$ with a contribution to the obscuredstar-formation of $\gtrsim 8\times10^{-4}\, \textrm{M}_\odot \textrm{yr}^{-1}\textrm{Mpc}^{-3}$. Some of the multiple systems have members with photometricredshifts consistent among them suggesting possible physical associations.Given their angular separations, these systems are most likely galaxyover-densities and/or early-stage pre-coalescence mergers. Finally, we present3mm LMT/RSR spectroscopic redshifts of six red-$Herschel$ galaxies at $z_{\rmspec}=3.85-6.03$, two of them (at $z \sim 4.7$) representing new redshiftconfirmations. Here we release the AzTEC and deblended $Herschel$ photometry aswell as catalogues of the most promising interacting systems and $z>4$galaxies.

Early Science with the Large Millimeter Telescope: a 1.1 mm AzTEC Survey of Red-$Herschel$ dusty star-forming galaxies