  Complete theoretical understanding of the most complex superconductors
requires a detailed knowledge of the symmetry of the superconducting energy-gap
$\Delta_\mathbf{k}^\alpha$, for all momenta $\mathbf{k}$ on the Fermi surface
of every band $\alpha$. While there are a variety of techniques for determining
$|\Delta_\mathbf{k}^\alpha|$, no general method existed to measure the signed
values of $\Delta_\mathbf{k}^\alpha$. Recently, however, a new 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 all k-space regions where
$\Delta_\mathbf{k}^\alpha$ 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 $\Delta_\mathbf{k}^\alpha$
it generates to the $\Delta_\mathbf{k}^\alpha$ determined from single-atom
scattering in FeSe where $s_{\pm}$ 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 $\Delta_\mathbf{k}^\alpha$ of opposite sign.
