  We present a strongly interacting quadruple system associated with the K2
target EPIC 220204960. The K2 target itself is a Kp = 12.7 magnitude star at
Teff ~ 6100 K which we designate as "B-N" (blue northerly image). The host of
the quadruple system, however, is a Kp = 17 magnitude star with a composite
M-star spectrum, which we designate as "R-S" (red southerly image). With a 3.2"
separation and similar radial velocities and photometric distances, 'B-N' is
likely physically associated with 'R-S', making this a quintuple system, but
that is incidental to our main claim of a strongly interacting quadruple system
in 'R-S'. The two binaries in 'R-S' have orbital periods of 13.27 d and 14.41
d, respectively, and each has an inclination angle of >89 degrees. From our
analysis of radial velocity measurements, and of the photometric lightcurve, we
conclude that all four stars are very similar with masses close to 0.4 Msun.
Both of the binaries exhibit significant ETVs where those of the primary and
secondary eclipses 'diverge' by 0.05 days over the course of the 80-day
observations. Via a systematic set of numerical simulations of quadruple
systems consisting of two interacting binaries, we conclude that the outer
orbital period is very likely to be between 300 and 500 days. If sufficient
time is devoted to RV studies of this faint target, the outer orbit should be
measurable within a year.
