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There are 3 slightly different versions of the International Driving Permit: the 1926 Convention, the 1949 Geneva Convention, and the 1968 Vienna Convention. See https://en.wikipedia.org/wiki/International_Driving_Permit for details. You might find you need to apply for 2 permits. Which one(s) you need is dependant on which convention your destination countries have ratified.
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You do not need to apply multiple times.
The original question was if you need an international driving license per trip. This should not be necessary. As noted, there are international conventions for international driving licenses.
Nothing in those conventions says that a license would be limited for a single trip or country. The license is valid until its expiry date.
However, the overall picture is a bit more complicated:
Usually any travel guide (or your national automobile club) will know what the rules are for that country.