In studying communicative signals, we can think of flexibility as a necessary correlate of creativity. Flexibility enables animals to find practical solutions and appropriate behaviors in mutable situations. In this study, we aimed to quantify the degree of flexibility in the songs of indris (Indri indri), the only singing lemur, using three different metrics: Jaro Distance, normalized diversity, and entropy. We hypothesized that the degree and the co-variation of the flexibility of indris singing together would vary according to their status and sex. We found that dominant females were more flexible than dominant males when concatenating elements into strings (element concatenation). The number of different elements in a song contribution normalized by the contribution length (contribution diversity) of dominant individuals positively co-varied for seven duetting pairs. Non-dominant individuals were more variable in element concatenation than dominant individuals, and they were more diverse in phrase type than dominant females. Independently from sex and status, individual contributions did not differ in entropy (a measure of the predictability of contributions). These results corroborate previous findings regarding the dimorphism by sex and by status of individual contributions to songs. Thus, they shed light on the presence and expression of flexibility in the behavior of a non-human primate species. Indeed, they potentially show an effect of social features in shaping vocal flexibility, which underlies many communication systems, including human language. We speculate that this degree of flexibility may account for creativity.