Can my son extend his 60-day tourist visa at any immigration office in Bangkok after overstaying?

How old is your son ??

And this post is exactly why correct terminology is so critical. 😮 🙁

I highly doubt the O/P's son is here on a "tourist visa" <- that they bought from a thai consulate in their country before they flew in. 😕

It is far more likely that they showed up here without any visa and were stamped in free stamp for 60 days on the visa exempt entry program

If indeed they are on a 60 day free stamp entry they do go to IT Square Laksi Plaza to get their 30 day extension for 1900baht.

BUT

as John Stanners correctly pointed out if they are indeed on a real tourist visa they do NOT go to IT Square and instead go to the main immigration office at Chaengwattana government complex building b..

This is where IT Square is located

If he has an actual visa he needs to go to Chaengwattana, if visa exempt he goes to Laksi

How old is your son?

OK, so he would like a 30 day extension, yet he will have overstayed. If you are lucky he will pay the fine and get the extension, however, they could just tell him to leave the country. he could have applied for the extension up to 30 days before (depending on office), so he did have plenty of time to do it.