Using a large suite of n -body simulations , we explore the discovery space for new satellites in the Pluto–Charon system . For the adopted masses and orbits of the known satellites , there are few stable prograde or polar orbits with semimajor axes a \lesssim 1.1 ~ { } a _ { H } , where a _ { H } is the semimajor axis of the outermost moon Hydra . Small moons with radii r \lesssim 2 km and a \lesssim 1.1 ~ { } a _ { H } are ejected on time scales ranging from several yr to more than 10 Myr . Orbits with a \gtrsim 1.1 ~ { } a _ { H } are stable on time scales exceeding 100 Myr . Near-IR and mid-IR imaging with JWST and ground-based occultation campaigns with 2–3-m class telescopes can detect 1–2 km satellites outside the orbit of Hydra . Searches for these moons enable new constraints on the masses of the known satellites and on theories for circumbinary satellite formation .