The use of tool sets constitutes one of the most elaborate examples of animal technology, and reports of it in nature are limited to chimpanzees and Goffin's cockatoos. Although tool set use in Goffin's was only recently discovered, we know that chimpanzees flexibly transport tool sets, depending on their need. Flexible tool set transport can be considered full evidence for identification of a genuine tool set, as the selection of the second tool is not just a response to the outcomes of the use of the first tool but implies recognizing the need for both tools before using any of them (thus, categorizing both tools together as a tool set). In three controlled experiments, we tested captive Goffin's in tasks inspired by the termite fishing of Goualougo Triangle's chimpanzees. Thereby, we show that some Goffin's can innovate the use and flexibly use and transport a new tool set for immediate future use; therefore, their sequential tool use is more than the sum of its parts.