Is it possible to have drop-down multiple choice option, where, if the choice the user wants is not available, a user can type in a new choice, and that choice is added to future surveys?
Drop-down type questions are typically used where the respondent has to make a single choice from a list of related options. It can be used for multiple selections, but this requires an extra step on the part of the respondent. There is no function that will allow you to add an OTHER write-in box to a drop-down list. I believe that your best alternative would be to use a check-box type question.
There are no standard functions that will allow a survey question to be automatically revised by a respondent’s input. It might be possible to develop a program that would do this, but I would advise against it. Respondents are not always consistent in their spelling and terminology, so modifying a question for future surveys should be a “hands-on” operation.