Our brain constantly integrates signals across different senses. Auditory-visual synaesthesia is an unusual form of cross-modal integration in which sounds evoke involuntary visual experiences. Previous research primarily focuses on synaesthetic colour, but little is known about non-colour synaesthetic visual features. Here we studied a group of synaesthetes for whom sounds elicit consistent visual experiences of coloured 'geometric objects' located at specific spatial location. Changes in auditory pitch alter the brightness, size, and spatial height of synaesthetic experiences in a systematic manner resembling the cross-modal correspondences of non-synaesthetes, implying synaesthesia may recruit cognitive/neural mechanisms for 'normal' cross-modal processes. To objectively assess the impact of synaesthetic objects on behaviour, we devised a multi-feature cross-modal synaesthetic congruency paradigm and asked participants to perform speeded colour or shape discrimination. We found irrelevant sounds influenced performance, as quantified by congruency effects, demonstrating that synaesthetes were not able to suppress their synaesthetic experiences even when these were irrelevant for the task. Furthermore, we found some evidence for task-specific effects consistent with feature-based attention acting on the constituent features of synaesthetic objects: synaesthetic colours appeared to have a stronger impact on performance than synaesthetic shapes when synaesthetes attended to colour, and vice versa when they attended to shape. We provide the first objective evidence that visual synaesthetic experience can involve multiple features forming object-like percepts and suggest that each feature can be selected by attention despite it being internally generated. These findings suggest theories of the brain mechanisms of synaesthesia need to incorporate a broader neural network underpinning multiple visual features, perceptual knowledge, and feature integration, rather than solely focussing on colour-sensitive areas.