The aim of the paper is to propose a robust model of interpersonal argumentation (IP). The IP-arguments directly address participants of communication, i.e. they refer to speech acts rather than to propositional contents. Argumentation theory recognizes several IP-arguments, e.g. argument from position to know or ad hominem arguments. The model proposed in the paper enables to describe references to different types of speech acts – not only assertives, but also commissives and directives. The IP-arguments are assumed to be warranted by the component of authorizing an agent to perform a given speech act. Consequently, the wider class of IP-communication can be expressed in the extended model, such as e.g. the structure of generic ad hominem can be explicitly represented as the undercutter.