The production of a low emittance muon beam is interesting for muon collider projects. In such context we study the production of positive and negative muon beams at 22 GeV, from ${e}^{+}$ beam-vs-fixed target collisions, with a very small transverse and longitudinal emittance of $25\text{ }\text{ }\ensuremath{\pi}\text{ }\mathrm{nm}\text{ }\mathrm{rad}$ and $3\ifmmode\times\else\texttimes\fi{}1\text{ }\text{ }\ensuremath{\pi}\text{ }\mathrm{mm}\text{ }\mathrm{GeV}$, respectively. In order to cope with the small conversion efficiency of positrons into muon pairs and the divergence of the beams, we connect thin targets by a quadrupole-only transport line common to three beams (${\ensuremath{\mu}}^{+}$, ${\ensuremath{\mu}}^{\ensuremath{-}}$, and ${e}^{+}$) at two different energies ($\ensuremath{\mu}$ at 22 GeV and ${e}^{+}$ at 44 GeV), where the line is specially designed to match the muon beam phase space over $\ifmmode\pm\else\textpm\fi{}5%$ energy spread and to mitigate the effect of multiple scattering with the targets on all beams. The transport line allows us to use a larger fraction of target material, increasing the muon population by a factor of 10 per positron bunch and splitting the power deposition over 20 to 40 targets, while keeping the muon beam emittance equal or similar to one from a single thin target of 1% of a radiation length. It might be possible to integrate this line into an accumulator ring in order to increase the muon bunch population over hundreds of positron bunches.