We present a general formal model called MODIA that can tackle a central challenge for autonomous vehicles (AVs), namely the ability to interact with an unspecified, large number of world entities. In MODIA, a collection of possible decision-problems (DPs), known a priori, are instantiated online and executed as decision-components (DCs), unknown a priori. To combine their individual action recommendations of the DCs into a single action, we propose the lexicographic executor action function (LEAF) mechanism. We analyze the complexity of MODIA and establish LEAF’s relation to regret minimization. Finally, we implement MODIA and LEAF using collections of partially observable Markov decision process (POMDP) DPs, and use them for complex AV intersection decision-making. We evaluate the approach in six scenarios within an industry-standard vehicle simulator, and present its use on an AV prototype.