Yes, you can request an extension of your stay in the US on a tourist visa by filing Form I-539, which is an application to extend or change non-immigrant status, with USCIS before your authorized stay on your I-94 record expires. You should apply at least 45 days before your I-94 expires to avoid issues with your immigration status and potential penalties like being banned from future travel to the US. You will need supporting documents and a valid reason for the extension and must pay a filing fee.