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Abstract Complete theoretical understanding of the most complex superconductors requires a detailed knowledge of the symmetry of the superconducting energy-gap$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ ${\Delta }_k^{\alpha }$, for all momentakon the Fermi surface of every bandα. While there are a variety of techniques for determining$$|{\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha |$$ $\mid {\Delta }_k^{\alpha }\mid$, no general method existed to measure the signed values of$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ ${\Delta }_k^{\alpha }$. Recently, however, a technique based on phase-resolved visualization of superconducting quasiparticle interference (QPI) patterns, centered on a single non-magnetic impurity atom, was introduced. In principle, energy-resolved and phase-resolved Fourier analysis of these images identifies wavevectors connecting allk-space regions where$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ ${\Delta }_k^{\alpha }$has the same or opposite sign. But use of a single isolated impurity atom, from whose precise location the spatial phase of the scattering interference pattern must be measured, is technically difficult. Here we introduce a generalization of this approach for use with multiple impurity atoms, and demonstrate its validity by comparing the$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ ${\Delta }_k^{\alpha }$it generates to the$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ ${\Delta }_k^{\alpha }$determined from single-atom scattering in FeSe where s_±energy-gap symmetry is established. Finally, to exemplify utility, we use the multi-atom technique on LiFeAs and find scattering interference between the hole-like and electron-like pockets as predicted for$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ ${\Delta }_k^{\alpha }$of opposite sign.