Stability of planetary, single M dwarf, and binary star companions to Kepler detached eclipsing binaries and a possible five-body system

In this study, we identify 11 Kepler systems (KIC 5255552, 5653126, 5731312, 7670617, 7821010, 8023317, 10268809, 10296163, 11519226, 11558882, and 12356914) with a flip-flop effect in the eclipse timing variations O - C diagrams of the systems, report on what these systems have in common and whether these systems are dynamically stable. These systems have previously reported high eccentric binary stars with highly eccentric third bodies/outer companions. We find that all of the additional bodies in the system are dynamically stable for the configurations previously reported and are therefore likely to exist as described. We also provide additional evidence of KIC 5255552 being a quadruple star system composed of an eclipsing binary pair and non-eclipsing binary pair with the possibility of a fifth body in the system. With the advent of the NASA's Transiting Exoplanet Survey Satellite (TESS) exoplanet survey, its precision photometric monitoring offers an opportunity to help confirm more local eclipsing binary star companions, including planets.