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.
(Hyphen korner: Note that in each case, you can use a hyphen if you want (just as with any compound). So, for example multiple-choice exam. Makes no difference.)
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 But those are just silly, of course.