Birds and bats are extremely adept flyers: whether in hunting prey, or evading predators, post-stall manoeuvrability is a characteristic of vital importance. Their performance, in this regard, greatly exceeds that of uncrewed aerial vehicles (UAVs) of similar scale. Attempts to attain post-stall manoeuvrability, or supermanoeuvrability, in UAVs have typically focused on thrust-vectoring technology. Here we show that biomimetic wing morphing offers an additional pathway to classical supermanoeuvrability, as well as novel forms of bioinspired post-stall manoeuvrability. Using a state-of-the-art flight simulator, equipped with a multibody model of lifting surface motion and a delay differential equation (Goman-Khrabrov) dynamic stall model for all lifting surfaces, we demonstrate the capability of a biomimetic morphing-wing UAV for two post-stall manoeuvres: a classical rapid nose-pointing-and-shooting (RaNPAS) manoeuvre; and a wall landing manoeuvre inspired by biological ballistic transitions. We show that parametric variation of nonlinear longitudinal stability profiles is an effective open-loop strategy to explore the space of post-stall manoeuvres in these types of UAVs; and it yields insight into effective morphing kinematics to enable these manoeuvres. Our results demonstrate the capability of morphing-based control of nonlinear longitudinal stability to enable complex forms of transient supermanoeuvrability in UAVs.