Over a mission lifespan, there are several phases where a spacecraft may underspend its fuel budget, leaving a limited but non-negligible amount of propellant at the end of the nominal mission timeline, unlocking possibilities to perform an add-on mission with a profile contrastive to the nominal. The present research was prompted by example of the ESA GAIA mission, where the remaining propellant generated discussion for such secondary science. One option explores Near-Earth Object (NEO) encounters from the Sun-Earth L2 (SEL2) Lagrange Point within a 2-year departure window spanning 01/01/25 – 01/01/27. Mission requirements including limitations on total delta-v (up to 150 m/s), Time of Flight (TOF, up to 9 months), and relative flyby velocities (up to 5 km/s) acted as constraints to the trajectory designs. Two Mission Scenarios (MS) were assessed and utilised escapes along the SEL2 unstable manifolds. MS 1 employed an exterior transfer towards the first Aphelion point, whilst MS 2 considered an interior escape from SEL2, followed by an Earth-powered flyby before asteroid rendezvous. NEO filtering evaluated target asteroid reachability by assessing the Minimum Orbital Intersection Distance (MOID) between the spacecraft and the NEO against a threshold value calculated from delta-v mission constraints. Desirable traits such as the Absolute Magnitude were also considered. Across the two designs, 91 preliminary candidates were deemed potentially reachable from asteroid filtering-Pork chop plots were built to provide reliable starting guesses for the candidate flybys and pave the way for trajectory optimisation. The latter was achieved by employing a single shooting method with mission constraints cost functions. The 10 most desirable candidates from MS 1 and all 20 from MS 2 underwent the optimisation scheme. Of the 30 candidates evaluated, 14 asteroids met at least one mission constraint, 11 meeting the delta-v constraint. Of these 11, 9 had relative flyby velocities below 5 km/s. 2 NEOs from MS 2 returned feasible trajectories below 11 months, the closest to the TOF requirement. Generally, MS 1 returned a higher candidate yield but suffered in its TOF in comparison to MS 2. MS 2 had less than half the manifold transfer duration to MS 1 but provided difficulty in optimising, as the initial guess was not deterministic unlike MS 1. From just the initial batches, so far it was demonstrated that not only can asteroid flybys be achieved within this delta-v, but also they can be done for significantly less than 150 m/s if desired.