The social and cultural duality perspective suggests dual ordering of interpersonal ties and cultural similarities. Studies to date primarily focus on cultural similarities in interpersonal dyads driven by principles such as homophily and contagion. We aim to extend these principles for sociocultural networks and investigate potentially competing micro-principles that generate these networks, taking into account not only direct dyadic overlap between interpersonal ties and cultural structures, but also the indirect interplay between the social and the cultural. The empirical analysis utilizes social and semantic network data gathered through ethnographic studies of five creative organizations around Europe. We apply exponential random graph models (ERGMs) for multiplex networks to model the simultaneous operation of several generative principles of sociocultural structuring yielding multiplex dyads and triads that combine interpersonal ties with meaning sharing links. The results suggest that in addition to the direct overlap of shared meanings and interpersonal ties, sociocultural structure formation is also affected by extra-dyadic links. Namely, expressive interpersonal ties with common third persons condition meaning sharing between individuals, while meaning sharing with common alters leads to interpersonal collaborations. Beyond dyads, the dual ordering of the social and the cultural thus operates as asymmetrical with regard to different types of interpersonal ties. The paper shows that in addition to direct dyadic overlap, network ties with third parties play an important role for the co-constitution of the social and the cultural. Moreover, we highlight that the concept of network multiplexity can be extended beyond social networks to investigate competing micro-principles guiding the interplay of social and cultural structures.