  We present new long-term CCD photometry for EP And acquired during the period
2007 to 2012. The light curves display total eclipses at primary minima and
season-to-season light variability. Our synthesis for all available light
curves indicates that the eclipsing pair is a W-type overcontact binary with
parameters of q=2.578, i=83.3 deg, $\Delta T$=27 K, f=28 %, and l3=2~3 %. The
asymmetric light curves in 2007 were satisfactorily modeled by a cool spot on
either of the eclipsing components from a magnetic dynamo. Including our 95
timing measurements, a total of 414 times of minimum light spanning about 82 yr
were used for a period study. A detailed analysis of the eclipse timing diagram
revealed that the orbital period of EP And has varied as a combination of an
upward-opening parabola and two periodic variations, with cycle lengths of
P3=44.6 yr and P4=1.834 yr and semi-amplitudes of K3=0.0100 d and K4=0.0039 d,
respectively. The observed period increase at a fractional rate of
+1.39x10^{-10} is in excellent agreement with that calculated from the W-D code
and can be plausibly explained by some combination of mass transfer from the
primary to the secondary star and angular momentum loss due to magnetic
braking. The most reasonable explanation for both cycles is a pair of
light-travel-time effects driven by the possible existence of a third and
fourth component with projected masses of M3=0.25 Msun and M4=0.90 Msun. The
more massive companion could be revealed using high-resolution spectroscopic
data extending over the course of a few years and could also be a binary
itself. It is possible that the circumbinary objects may have played an
important role in the formation and evolution of the eclipsing pair, which
would cause it to have a short initial orbital period and thus evolve into an
overcontact configuration by angular momentum loss.
