<p>Behavioral innovativeness—the propensity of an individual organism or higher group to innovate—is frequently invoked as a measurable trait allowing for cross-species comparisons. Individuals or species are often regarded as more innovative or less innovative than others, implying that we can rank order the degree of innovativeness along a single dimension. This paper defends a novel multidimensional understanding of behavioral innovativeness in which innovativeness can be modulated with respect to the generation and capitalization of opportunities, as well as the effectiveness and depth of the innovative behaviors. Besides innovation being multidimensional, it is also multilevel. Here we show how innovativeness at one level (such as the species level) does not automatically translate to innovativeness at another (such as the organism level) and discuss why this matters for cross-species comparisons.</p>