The re-entry permit counters at both Don Mueang and Suvarnabhumi are open
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and there's no issue getting a re-entry permit from there before you leave
You don't need any documents IF you are not averse to paying 200baht extra above the price of the re-entry, you just need your passport π (single re-entry 1200, multiple re-entry 4000)
Now if that is too steep a price to pay for no documents needed re-entry, you can make a copy of your PDF visa, your entry stamp, the data page of your passport and have a filled out TM8 application for re-entry permit with a passport sized photo stuck to it (single re-entry 1000, multiple re-entry 3800)
I am questioning WHY you would want a multiple entry re-entry permit because the permit itself is only going to be good for the 90 days you're stamped in on now.. (it won't add any time to your current stamp, just let you back in on the same expiration date)
So unless you're going to travel out/in several times during this 90 days don't waste the money for the multiple re-entry. Get that AFTER you get the year extension inked in at the immigration office