Network analysis and machine learning techniques have been widely applied for building malware detection systems. Though these systems attain impressive results, they often are $(i)$ not extensible, being monolithic, well tuned for the specific task they have been designed for but very difficult to adapt and/or extend to other settings, and $(ii)$ not interpretable, being black boxes whose inner complexity makes it impossible to link the result of detection with its root cause, making further analysis of threats a challenge. In this paper we present RADAR, an extensible and explainable system that exploits the popular TTP (Tactics, Techniques, and Procedures) ontology of adversary behaviour described in the industry-standard MITRE ATT\&CK framework in order to unequivocally identify and classify malicious behaviour using network traffic. We evaluate RADAR on a very large dataset comprising of 2,286,907 malicious and benign samples, representing a total of 84,792,452 network flows. The experimental analysis confirms that the proposed methodology can be effectively exploited: RADAR's ability to detect malware is comparable to other state-of-the-art non-interpretable systems' capabilities. To the best of our knowledge, RADAR is the first TTP-based system for malware detection that uses machine learning while being extensible and explainable.