This paper seeks to investigate the effects of conflicting reference points across different dimensions of utility on effort exertion. Reference-dependent preference models so far have assumed additive separability across different dimensions of utility, which implies that agents respond to reference points in each dimension in isolation from one another. Challenging this assumption, this paper posits that agents consider multi-dimensional reference points in tandem: agents are less responsive to reference points if they have low probabilistic expectations of being able to concurrently achieve them and/or if they have difficulty reconciling them into a single baseline against which to evaluate outcomes. It refines the Koszegi-Rabin reference-dependent preference model to incorporate these effects and applies it to examine effort exertion under targets in different task performance dimensions. The original and refined model produce distinct predictions for optimal effort exertion, which are tested via a real effort experiment. However, the experimental results are inconclusive, finding some evidence of attenuation but which is not statistically significant nor robust. They do shed light on dynamics between internally conceived and externally imposed targets and how they enter into reference point formation which has bearing for target design and can be a promising new area of research for the future.