2

Since "二者択一の問題" is a multiple choice problem with 2 options, would it be understandable to say:
"三者択一の問題" --> multiple choice with 3 options
"四者択一の問題" --> multiple choice with 4 options
.....

would it also be a natural thing to say?

5

Yes, you can fill in any number in n 者択一, but it generally sounds too lofty, and the most common way to name it is n 択. "Multiple choice problem with n options" is often called n 択問題.

By the way, "multiple choice problem" itself is 択一問題, 選択問題, or 多肢選択問題.

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