<p>How can we develop an adequate scientific understanding of the minds of nonhuman animals? We argue for a methodology based on multi-dimensional profile accounts. Such accounts are already used for the comparative study of norm cognition, consciousness, empathy and causal cognition, among others. This methodology demands that a cognitive capacity is characterized by a set of independent dimensions where each dimension is connected to operationalizable empirical indicators. Based on the level of realization for each indicator the level of implementation of a dimension is determined for a species, resulting in a multi-dimensional profile for each species. We analyze what this methodology is committed to. Then, we argue that this methodology has several benefits over competing unidimensional methodologies, by overcoming intractable disagreements, capturing the evolutionary continuity of cognition, alleviating anthropocentrism, and delivering more informative accounts of animal cognition. By demonstrating how this multidimensional methodology can be fruitfully combined with a methodology which focuses on the search for natural kinds in comparative cognition, we address the most important objection to the multidimensional profile methodology. We conclude that multidimensional profile accounts of all complex cognitive capacities should be developed and then used to facilitate scientific understanding of animal minds.</p>