We present Malacopula, a neural-based generalised Hammerstein model designed to introduce adversarial perturbations to spoofed speech utterances so that they better deceive automatic speaker verification (ASV) systems. Using non-linear processes to modify speech utterances, Malacopula enhances the effectiveness of spoofing attacks. The model comprises parallel branches of polynomial functions followed by linear time-invariant filters. The adversarial optimisation procedure acts to minimise the cosine distance between speaker embeddings extracted from spoofed and bona fide utterances. Experiments, performed using three recent ASV systems and the ASVspoof 2019 dataset, show that Malacopula increases vulnerabilities by a substantial margin. However, speech quality is reduced and attacks can be detected effectively under controlled conditions. The findings emphasise the need to identify new vulnerabilities and design defences to protect ASV systems from adversarial attacks in the wild.