Reliance on animal foods must be reduced to improve planetary and human well-being. This research studied plant-based cheese alternatives (PBCA) relative to dairy cheese in a consumer taste test with 157 consumers in New Zealand. A case study approach used cream cheese (commercially available) as the focal product category (2 PBCA, 2 dairy) and implemented a multi-response paradigm (hedonic, sensory, emotional, conceptual, situational). “Beyond liking” insights were established, including drivers of liking (sensory, non-sensory) and sensory drivers of non-sensory product associations. Two consumer segments were identified, of which the largest (n = 111) liked PBCA and dairy samples equally (6.5–6.7 of 9). In this PBCA Likers cluster, the key sensory drivers of liking were ‘creamy/smooth mouthfeel’, ‘dissolves quickly in mouth’, and ‘sweet’, while a significant penalty was associated with ‘mild/bland flavour’. The non-sensory data contributed additional consumer insights, including the four samples being perceived as differently appropriate for 9 of 12 use situations, with PBCA being regarded as less appropriate. In the limited confines of this case on cream cheese, the findings show that PBCA need not be inferior to their dairy counterparts despite a general narrative to the contrary. Of note, the results were obtained among participants who were open to eating a more PB diet but were not vegetarian or vegan.