In this paper we deal with the activity of "offering a drink" as an exemplary case of complex activity that cannot be fully described as an expanded adjacency pair. Relying on a corpus of naturally occurring conversations among friends, we focus our attention on the sequential and multimodal organization of this activity. First, we focus on how the activity is launched through various resources. Then, we turn to subsequent trajectories of the interaction. We consider cases of negociations of the offer, and then recurrent cases in which the activity is locally suspended. This leads to discuss whether the moments of suspension should be considered as stopping the activity or as being a part of it. On the basis of a multidimensional approach, and specifically with a focus on gestural cues, we argue for the existence of a "meso-interactional whole" (cf. Psathas 1991) to which participants keep oriented.