Object permanence, the understanding that objects continue to exist while out of sight, has been extensively researched in human infants and animals. Cats have been shown to reach Stage 5 object permanence by passing successive visible displacement tests, but their understanding of Stage 6 object permanence is less clear. We tested 18 domestic cats on their understanding of Stage 4 (single visible displacement; SVD) and Stage 6 (invisible displacement; IVD) of object permanence in their home environment. Additionally, we investigated how person familiarity may influence study engagement. In SVD tests, the box manipulator (owner or researcher) hid a toy in one of two cardboard boxes for the cat to find. In IVD tests, we implemented a violation-of-expectancy procedure in which the box manipulator showed a toy re-appearing out of either a) the same box it was hidden in (consistent trials) or b) the box it was not hidden in (violation trials). Approximately half of the cats (56%) did not find the hidden toy in SVD trials, with 42% of these cats not attempting to find the toy, despite previous research demonstrating that cats can retrieve hidden objects in successive SVD tests. No predictors significantly influenced whether cats found the toy, or which box was checked first (toy or empty box). In IVD trials, we unexpectedly found that cats were more likely to play with and had longer gaze durations towards the toy and display more toy box-directed behaviours in consistent trials than violation trials. Similarly, we found that cats were more likely to display toy and empty box-directed behaviours in trials where the researcher acted as the box manipulator. Other factors such as breed, outdoor access, cat sex and the first person to act as the box manipulator also influenced toy-directed behaviours. We discuss the complexity of person familiarity in research contexts and highlight some methodological challenges in studying cat cognition.