BeyonCE (Beyond Common Eclipsers) explores the large parameter space of eclipsing disc systems. The fitting code reduces the parameter space encompassed by the transit of circumsecondary disc (CSD) systems with azimuthally symmetric, non-uniform optical-depth profiles to constrain the size and orientation of discs with a complex sub-structure. BeyonCE does this by rejecting disc geometries that do not reproduce the measured gradients within their light curves.