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 those are just silly of course.