We developed a multi-domain spoken dialogue system that can handle user requests across multiple domains. Such systems need to satisfy two requirements: extensibility and robustness against speech recognition errors. Extensibility is required to allow for the modification and addition of domains independent of other domains. Robustness against speech recognition errors is required because such errors are inevitable in speech recognition. However, the systems should still behave appropriately, even when their inputs are erroneous. Our system was constructed on an extensible architecture and is equipped with a robust and extensible domain selection method. Domain selection was based on three choices: (I) the previous domain, (II) the domain in which the speech recognition result can be accepted with the highest recognition score, and (III) other domains. With the third choice we newly introduced, our system can prevent dialogues from continuously being stuck in an erroneous domain. Our experimental results, obtained with 10 subjects, showed that our method reduced the domain selection errors by 18.3%, compared to a conventional method.