We present new long-term CCD photometry for EP And acquired during the period 2007-2012. 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=27K, f=28%, and l_3_=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 82yr was 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 P_3_=44.6yr and P_4_=1.834yr and semi-amplitudes of K_3_=0.0100days and K_4_=0.0039days, respectively. The observed period increase at a fractional rate of +1.39*10^-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 M_3_=0.25M_{sun}_ and M_4_=0.90M_{sun}_. 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.