Assuming you are from INDIA , you need the 60 days TR visa issued from India. The VOA is not convertible to any other kind of visa in case of Indian passport.
If the primary Employer agrees and the issues the NOC and then you go to DOL with that the "second job" can be updated on the WP. So ppl having WP issued by A ( primary employer ) can also work for B , if A has no objection and issues the NOC.
If It's all about visa then you better be very cautious with schools and the paperwork. "Assuming" you hold Indian passport ,you will have to jump over hoops to pull an Ed visa INSIDE Thailand. It's not impossible but difficult and you might have to cough heavy price around 25K for FIRST three months and around 12K for every 90 days renewals. These are Bkk rates though. Good luck
Well that is NOT a visa run . In fact there is no term visa run that exists for Indian paaaport holders. If after the expiry of your 60 days or 15 days visa you go back and apply the VERY NEXT DAY for another 60 days T visa you may very well get a VOID stamp. However , you can fly to Cambo / Laos and stay there 30 days and come back again for 15 days , thats the max. Indians can do