Would taking up an associate's degree after finishing your bachelor's harm your resume?
Having multiple degrees would by no means harm your resume. Listing a degree that has absolutely no relation to the job you are applying for may. The answer to this question depends on what you are trying to accomplish, whether it be to have another line item on your resume or to actually obtain a degree related to the field in which you entering. It never hurts to learn more. The only thing you may lose 

http://careersteering.com/executiveresume/education-on-resume/
http://www.genpink.com/10-things-to-quit-putting-on-your-resume/