Can I renew my tourist visa or get a 30-day extension on the same day it expires?

You can apply for a 30 day extension on a 30 day visa exempt entry stamp too at the immigration office for 1900baht. You can do it before or ON the day you're "admitted until" ..

So you're now on a 60 day tourist visa and you want to apply for a 30 day extension?

You can apply for it at most immigration offices when you have 30 days or less left on your current stamp. There is no benefit waiting until your current stamp is expiring because they ADD the 30 day extension onto your expiration date.

You can go the last day if you want to..