In this paper, we rely on multiple correspondence analysis (MCA) to explore a complex ecosystem of Italian innovative enterprises. In this respect, we analyze more than 11.000 innovative SMEs and start-ups. We find that the Italian innovation ecosystem is mainly structured along two dimensions. The first and most significant dimension emphasizes the opposition between structured institutional elements that are typical of SMEs and leaner, more flexible arrangements closer to the start-ups. The second axis is that of social inclusiveness and innovation as opposed to sociocultural sedimentation, which is more representative of well-established SMEs in the industrial/artisanal sector. An additional analysis of concentration ellipses revealed that start-ups are prone to rely on higher female representation and are closer to the service sector category. If we treat the latter as a proxy category for incubators, which were all designated as services, then the unfortunate conclusion is that Italian innovative enterprises tend to lose their social innovativeness aspects, which include but are not limited to social inclusivity, once past the start-up phase. The ramifications of these dynamics are yet to be sufficiently understood in relation to the broader ability of enterprises to innovate.