Ridesharing options for secondary payloads to be delivered to regions beyond geostationary altitude are increasingly available with propulsive evolved expendable launch vehicle secondary payload adapter rings. The preliminary mission design for secondary payloads must consider the variability of the dropoff orbit orientation: a factor that is a function of the primary mission. In this analysis, assume that the dropoff orbit is an Earth-centered geosynchronous transfer orbit (GTO). Then, propellant-efficient transfers to periodic and quasi-periodic orbits near the Sun–Earth Lagrange point are constructed from a range of GTO orientations. Dynamical structures (such as hyperbolic invariant manifolds) associated with orbits near Sun–Earth Lagrange point are leveraged to identify and summarize various types of transfer opportunities.