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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 develop a guidance method for these manoeuvres, based on parametric variation of nonlinear longitudinal stability profiles, which allows efficient exploration of the space of post-stall manoeuvres in these types of UAVs; and yields insight into effective morphing kinematics to enable these manoeuvres. Our results demonstrate the capability of biomimetic morphing, and morphing control of nonlinear longitudinal stability, to enable advanced forms of transient supermanoeuvrability in UAVs.