What is the procedure for extending a Multi Entry Visa when traveling to another country?

You can enter Thailand and unlimited number of times until the end date on your visa. Each time you enter you'll be stamped in for the full number of days depending on which visa you have.

If your visa is a full page sticker in your passport then make sure you let them know you're entering with the visa in your passport.

If you have an e-visa make sure you have it printed and again let them know you have a visa and hand them the printout with your passport.

In all cases make sure you check your stamp after you step away to make sure it's correct. There have been multiple reports of people getting the incorrect stamp and not noticing until they're too far away to fix it.