Yes, it is possible to extend your stay in Singapore after completing your studies. If you wish to pursue further education, you can apply for a new student visa for your next course. Alternatively, if you want to explore employment opportunities, you may need to transition to a different visa category, such as an Employment Pass (EP) or a Work Holiday Pass (WHP). It's important to familiarize yourself with the specific requirements and procedures for each visa category to ensure a smooth transition.