While insight into visitor engagement proliferates, understanding the effect of engagement on visitors’ intention to revisit cultural heritage sites across physical, technology-enhanced, and virtual formats remains limited, leaving a significant gap in the literature. Addressing this gap, this research investigates how visitors’ cognitive, emotional, and behavioural engagement affect their traditional physical (RI), technology-enhanced on-site (T-RI), and purely virtual (V-RI) revisit intentions. In collaboration with the Archaeological Park of Pompeii (Italy), we surveyed international visitors and obtained 572 valid responses. Structural equation modelling (SEM) results reveal that emotional engagement consistently predicts all three revisit intentions, cognitive engagement significantly influences physical revisit intention, and behavioural engagement primarily drives virtual revisit intention. This research advances theoretical insight into the differential predictive role of engagement dimensions across distinct forms of revisit intention, while informing cultural heritage sites evaluating or expanding visitation formats.