You're forming a two-word adjective which describes something. There's no "s".

Multiple choice question.

Multiple choice questions.

Multiple choice exam.

Multiple product packaging.

Multiple seat aircraft.

Multiple restrike starter motor.

Multiple restrike fuses.

Note that in each case, you can use a hyphen is you want (just as with any compound).  So, Multiple-choice exam, etc. Makes no difference.

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Note - you could make up very obscure tortured situations where, the "choice" part **IS A NOUN** and the "multiple" is just an adjective.  Something like this .. *"in life she faced multiple choices at the same time"*  or *"the lightning struck once, then restruck, then restruck again, so, we had multiple restrikes after the original strike."* but those are just silly of course.