Scoot airlines have changeable tickets for an additional $20 Singapore. Just fair difference applies. So when fly you can show them a ticket out in 30 days and then change it once you get to Thailand. I assume you plan to go back to another SE Asian country first before flying home? I was asked at the airports of my exit flights on some of trips around the area.
If you have spent 180 days in past 12 months as a regular tourist in country then at the main airports in particular is triggering an alert to pull you aside for questioning.
apply for your regular 30 day extension first at your local immigration. Every entry is entitled to one 30 day extension on a tourist visa or visa exempt. After that is expired you need to leave the country and do the border re-entry process.
Although there’s no offical limits other than the 2 land borders, be wary about entering via the 2 major airports in particular if you have spent over 180 days in country in the past 12 months. The immigration officers at the Bangkok airports in particular are at their discretion pulling aside people who have been in country over 180 days as a regular tourist. It happened to me on 1st May and I needed approval by their superior to enter. If you are over that limit then you really need to look at other options to extending a visit ie making use of the 2 land border bounces (with a border run company) if not yet used, or applying for METV well in advance of a long planned trip.
If you are wanting another 60 days here and haven’t entered by land already twice this year on visa exempt then you could just do a border run using one of those border run company’s that get you out and back in one a day trip. It will get you 30 days with 30 more extension at immigration.