I know it is also possible to get a re-entry permit in both int. airports.
Is it possible also on land-borders, specifically, Laos via Nong-Khai?
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It is possible to get a re-entry permit at an immigration office (e.g. the government centre at Chaengwattana in Bangkok), but from memory I don't think it's possible at the borders.
Please be aware that a re-entry permit does not affect the date by which you must leave Thailand - it merely allows you to exit and re-enter as if it was your previous entry. So if you get a 90-day stamp when entering Thailand, then get a re-entry permit and go out then come back, your previous 90-day stamp is still valid, and you must exit within 90 days of your original entry.
Yes, it is possible.
No, you cannot do this on land.
In the international airport, they have a special re-entry desk. However, for land border, you should have a origin country. In the case of Laos, you should come from Laos. This means, when you leave Thailand, you should enter Laos and leave Laos to be eligible to enter Thailand again.