Can I extend my 60-day visa in Thailand or convert it to an ED visa?

Now on to the topic of whether you can get an in country Non-ED visa issued from the immigration office on a covid extension.

You need to be talking to the school you're thinking of studying at because whether you can or can't totally depends on the school that you're studying at and the immigration office you'd be using to get the 90 day Non-ED visa

First lets get you on track with what you have in your passport

You don't have ANY visa :O LOOK at your stamp and you will see it says "extension of stay permitted until" and then has a date stamped. That is NOT a visa, it's an extension..

Now that we got that sorted out you can indeed apply for another 60 day extension (using the same copies and documents you used before) for 1900baht. You need to do it before this current stamp runs out, BUT don't do it too early because the date you apply for the next 60 days is the date it starts so applying too early will make you lose days on your current stamp (most people go 3 or 4 days before their current stamp expires)

You have an extension not a visa and yes you most likely can extend again