In this paper, the external and internal cooperation determinants of the four types of innovation – product, process, organisational and marketing – are studied from the perspective of small and medium-sized enterprises (SMEs). From a theoretical standpoint, taking into account the dual nature of cooperation, cooperation determinants can be divided into two groups: external - comprising triple helix entities: universities, governments and industry, and internal – comprising employee personality traits: decision-making autonomy, creativity, willingness to cooperate, openness to changes, risk-taking and social empathy. Additionally, three control variables were considered: age, size and sector of economic activity. The data examined comes from an empirical study of a randomly selected representative sample of 1286 SMEs in the Kuyavian-Pomeranian voivodeship, a region in central-northern Poland. The empirical research was carried out between June and September 2019 using the CAPI method. The multivariate probit regression model was used to analyse the obtained data. The results indicate that only two factors directly connected with the triple helix are common and significant determinants explaining all SME innovations. These are cooperation with public administration in the field of financial support, and cooperation with clients. In turn, significant variation was observed in terms of personality traits being an essential element of internal cooperation that may influence SME innovations. A positive impact on the probability of implementing three of the four types of innovation was observed for two personality traits, namely creativity and social empathy.