Can I apply for a 60-day Covid extension and then a 1-month extension on my Thai TV visa?

Have to do 30 day first with accommodation before can extend.

I'd say go apply for the 30 day extension NOW (they will add it to the expiration date you have in your passport now) and then before the 29th of July apply for the covid extension

You can apply for an in country 90 day Non-O visa at MOST immigration offices by meeting the financial requirements and having 15 days or more left on your 60 day entry stamp, your 30 day extension stamp OR your 60 day covid extension stamp :O :P

when does your current 60 day entry stamp expire?

you can't get them out of sequence, meaning IF you apply for the 60 day covid extension you give up the ability to use the 30 day extension.