Automated question generation has made great advances with the help of large NLP generation models. However, typically only one question is generated for each intended answer. We propose a new task, Multi-Question Generation, aimed at generating multiple semantically similar but lexically diverse questions assessing the same concept. We develop an evaluation framework based on desirable qualities of the resulting questions. Results comparing multiple question generation approaches in the two-question generation condition show a trade-off between question answerability and lexical diversity between the two questions. We also report preliminary results from sampling multiple questions from our model, to explore generating more than two questions. Our task can be used to further explore the educational impact of showing multiple distinct question wordings to students.