Can I Extend My 3-Month Single Entry Visa Twice in Thailand?

You need to understand the validity of a single entry tourist visa which is 3 months from the date it's issued <- meaning you have 3 months to ENTER thailand.

When you enter the country you will get stamped in for 60 days like everyone on a tourist visa does.

You can extend that 60 day entry ONCE for 30 days at the immigration office then you are done and need to leave the country to get a new visa or enter on a new entry stamp.