Can I apply for a 60-day Covid extension on my Tourist Visa in Thailand?

That is between you and your immigration office.

MOST offices are requiring people who have recently entered on 45 day visa exempt or 60 day tourist visas to get their 30 day 'regular' extension FIRST.

Some offices will let you apply for the 60 day covid extension BUT they tell you it will start the date you apply rather than be added to your current expiration date (like the 30 day regular extension is)

Check with your immigration office once you out of ASQ.