Comparative cognition aims at unfolding the cognitive processes underlying animal behavior and their evolution, and is concerned with testing hypotheses about the evolution of the brain and intelligence in general. It is a developing field still challenged by conceptual and methodological issues. Systematic cross-species comparisons of cognitive abilities, taking both phylogeny and ecology into account are still scarce. One major reason for this is that it is very hard to find universally applicable paradigms that can be used to investigate the same cognitive ability or "general intelligence" in several species. Many comparative paradigms have not paid sufficient attention to interspecific differences in anatomical, behavioral and perceptual features, besides psychological variables such as motivation, attentiveness or neophobia, thus potentially producing misrepresentative results. A new stance for future comparative research may be to establish behavioral and psychological profiles prior or alongside to comparing specific cognitive skills across species. Potentially revealing profiles could be obtained from examining species differences in how novel experimental (extractive foraging) tasks are explored and approached, how solutions are discovered and which ones are preferred, how flexibly multiple solutions are used and how much individual variation occurs, before proceeding to more detailed tests. Such new comparative approach is the Multi-Access-Box. It presents the animal with a novel problem that can be solved in several ways thus offering the possibility to examine species differences in all the above, and extract behavioral and perceptual determinants of their performance. Simultaneously, it is a suitable paradigm to collect comparative data about flexibility, innovativeness and problem solving ability, i.e., theoretical covariates of "general intelligence", in a standardized manner.