John Searle’s account of collective intentions in action appears to have all the theoretical pros of the non-reductivist view on collective intentionality without the metaphysical cons of committing to the existence of group minds. According to Searle, when we collectively intend to do something together, we intend to cooperate in order to reach a collective goal. Intentions in the first-person plural form therefore have a particular psychological form or mode, for the we-intender conceives of his or her intended actions as singular contributions by means of which – or: by way of which – a collective goal is pursued. Accordingly, we-intentions are held to have a psychological mode with a “collective goal by means of (viz. by way of) singular contribution” structure, which makes them primitive and irreducible to intentions in the I-form. It is further contended that, albeit primitive and irreducible, we-intentions are not the mental states of an alleged group mind but always of an individual’s mind. This paper targets Searle’s claim of irreducibility by developing an argument whose aim is to show that, pace Searle, it is possible to track the idea of intentions with a psychological mode structured in terms of “collective goal by means of (viz. by way of) singular contribution” back to the concept of intentions in the I-form. The argument mainly relies on the idea that Searle’s technical expressions “being a collective goal by means of singular contribution intention in action” or “being a collective goal by way of singular contribution intention in action” are susceptible to conceptual analysis. The upshot of this analysis is that we-intentions can be reduced to complex bundles of mental states, all of which come in the first-person singular form. If this argument is sound, Searlean we-intentions do not belong to a primitive kind of mental states.