Some students are attracted to the idea of double majoring because they think it will look impressive on their resumes and will help them get into a better graduate school or land a better job. The reality is that graduate schools and employers are far more interested in what you know, how well you can reason, and how well you can communicate than they are in multiple majors or minors. You should be most concerned with selecting the courses that will give you the best possible preparation for life after Stetson and not fixate on padding your transcript with an extra major or multiple minors. A high quality education will shine through in your resume without the extra padding.
Developing robust skills in more than one academic area is generally good because interdisciplinary efforts are often needed to properly address the important issues and problems that arise today. It does not, however, require you to complete a double major or even a minor. All that it requires is to take carefully selected courses in a second field. There are students in the College of Arts and Sciences who demonstrate this every year by incorporating an interest in an outside field into the design of their Senior Projects. A Senior Project in Philosophy, for instance, might use literary texts, artworks, Facebook postings, or science experiments as the subject of inquiry. A Psychology project might deal with responses to art, and a Physics project may develop a computer model that allows the energy usage of a neural cell to be investigated. The total package of experience in completing one major, carefully selected courses in a second field, and a single Senior Project that draws on both will be compelling to any graduate program or employer. The key is to work closely with your faculty adviser and teachers to develop clear academic goals, and then to reevaluate those goals every semester.
If you have looked carefully at the courses that appear to be best for you and they add up to something that comes close to completing two separate majors, then attempting to do two majors may make sense for you. However, it still may not be the best choice. Invariably there will be some courses in one of the majors that do not fit very well with your interests and goals that are required for that major. Those courses will prevent you from taking electives that are a better match with your goals (e.g. upper level electives in either of the majors, an advanced writing course, a supporting course in a related field, etc.). Keep in mind that the goal is to choose the courses that provide the best education for your goals and interests.
If double majoring still looks like the best choice for you, then work with advisers in both departments to map out when you would need to take the required courses to ensure that you can still graduate at the intended time. You will have to satisfy all requirements for both majors, including Senior Project. If the two majors have sufficient overlap in their interests it may be possible to design a senior project that will work for both majors, but this cannot be guaranteed, so you should build a plan around two separate projects. Even if you are able to do a single project, both departments may require you to complete the courses associated with their senior projects. Be aware that your plan will have to be reevaluated every semester because two courses that you are required to take may be taught at conflicting times. You may ultimately have to make a choice between completing only one major or delaying graduation by a semester or two to complete the requirements for the second major.
A request for declaring a double major within one College/School is made to the appropriate academic dean using the form that is available in the Registrar's office. You will be required to consult with advisers from both majors. Your academic ability and performance will be a factor that is considered prior to the request being approved.
A double major that spans two College/Schools is considered a Dual Degree, which has additional requirements. You should consult with the Registrar about the requirements for a Dual Degree.