This paper investigates the use of solar sailing propulsion to visit as many co-orbital near-Earth asteroids (NEAs) as possible, within a fixed time-frame. This research builds on previous publications, which have shown solar sailing to be a suitable propulsion method to visit NEAs. The dynamics of this problem are modelled within the Solar Sail Augmented Circular Restricted Three-Body Problem (CR3BPS), and assume a near-term solar sailing technology level. A sequence generation algorithm is developed which generates trajectories to visit multiple co-orbital NEAs beginning at either the artificial co-linear equilibrium point SL1 or SL2. This algorithm develops trajectories with fixed controls to transfer between target asteroids, using Monte Carlo simulations to propagate a wide range of random combinations of settings before selecting those that perform the best. It is shown that the tuning performed within this research can generate a trajectory that enables 18 asteroid fly-bys within the selected nominal mission lifetime of ten years. Following this sequence generation, the first fly-by of the trajectory is optimised as proof of concept that each leg of the trajectory can be optimised for fly-by distance and velocity. An optimal control problem is developed, which is then implemented and solved using direct pseudospectral methods. The solution to this optimal control problem reduces the fly-by distance by 99.95 %, down to 158.73 km, while reducing the fly-by velocity by 9.68 % to 4.33 km/s.