Actually, I can tell you about one career that combines, STEM, art and the humanities; it is a career path that I once followed before I became an art teacher (I'll tell you why I switched later in my response).
The field is Art Conservation, and an art conservator is a museum professional who works (usually) in a museum to take care of the physical needs of an art collection. (This is not to be confused with an art curator, who takes care of and studies the historical aspects of an art collection. ) The physical needs range from understanding the right environment for fragile art objects in terms of humidity and light levels, to repairing art objects that have become damaged or have deteriorated due to age, to restoring art objects back to a former state so that they can be viewed and understood better by the public. As you can image, there is a variety of museums and art objects out there, and conservators often specialize in areas such as paintings, objects, paper objects (books, documents, etc.) and architecture.
To treat and take care of the artworks, a conservator needs to know about the composition and material science behind the artworks, and they need to understand how the modern day products, such as glues, will affect them. So for most conservation programs you need to have classes in General and Organic chemistry, as well as classes in art history, and evidence of good hand skills by taking studio art classes and being able to show your artwork. Many conservators have an undergraduate degree in art history, studio art , or chemistry, and fill in the above classes as needed.
After getting their BA or BS degree, conservators will enroll in a master degree program in conservation, which usually takes a total of three years; 2 years of classes and one year of an internship in a museum. Many if not most applicants have volunteer experience in a museum conservation lab before applying to a conservation school. Conservation schools only accept a very limited number of students per year, so they are VERY competitive to get into, and this museum experience has become a de facto requirement for some schools. I studied archaeological conservation at the University of London, but there are schools in the US and Canada. The programs for masters programs in conservation are:
University of Delaware (which comes with a full scholarship)
New York University, NY (New York City)
University of New York in Buffalo (Buffalo, NY)
Queens University, Kingstown, Ontario Canada
Scripps College in Claremont CA (a woman's college) has started an undergraduate program in conservation, this is something new. There may be other schools with undergraduate programs in conservation or museum studies that I don't know about, so check this out; however, I'm not sure if an undergraduate degree in conservation is enough to land a job as a conservator; I think museum will still want a graduate degree.
After getting their masters degree in conservation, most conservators apply for paid (usually very low pay) post-graduate fellowships at museums before they can get their full time job at a museum. I had two post graduate fellowships, which were really great learning experiences, which helped me land a full time museum job as a conservator. There are also conservators who open their own conservation studios and do private work.
The pay is about what museum workers make; you'll make a decent living doing something you love.
If it sounds like it is a long road to becoming a conservator, it is. No doubt about it. However, if you like science, have a passion or least a strong interest in art and history, and like using your hands, then this can be a very rewarding field to pursue. I left conservation because I discovered I liked working more with people than objects, so I went into art education and was very happy. I still love museums and archaeology, but I was happy as an art teacher working with kids.
For more information, I suggest you visit the American Institute of Conservation's website. www.aic.org
I hope this helps! Best wishes.