Is is possible to change a survey question from single response to multiple response without effect the data I have already collected?
If you change the question type you will probably lose all of the data you have already collected. See the documentation for details – http://help.surveygizmo.com/help/article/link/make-survey-edits#editing-a-live-survey.
I think that your best option would be to temporarily close your survey, disable the old question (http://help.surveygizmo.com/help/article/link/disable-questions, http://help.surveygizmo.com/help/article/link/delete-or-disable), build the new question in its place, and reopen the survey. Disabling the old question means it will not appear to respondents, but the existing response data will be preserved.