I am an Amherst alum so it is difficult to answer your earlier questions on what is available at Amherst now. I suggest you talk with current STEM students and faculty in your area of interest. I do know that Amherst students can choose to work over the summer to do research projects on campus or else seek opportunities in laboratories in universities where they live or at a university where they have some specific research interest. In my case, I lived outside Boston, and worked at a laboratory at Harvard Medical School during the summer of my sophomore year. I became very fascinated by my work so I was able to work in my lab for the ensuing year and took courses at MIT before returning to Amherst for my junior year. Years later, when I ran my own medical research labs at Harvard and NIH, I had students from Amherst and other colleges participate in summer internships. I actually recommend students from LACs to have some experience at a major research university during or after college if they are contemplating a career in that direction. I think LACs are a wonderful place to learn science and to think critically and broadly. However, in terms of functioning in the competitive research world, it is good to have some exposure to what life is like on a daily basis before diving in and pursuing a Ph.D. or a combined M.D./Ph.D.
Here is a link for engineering at Amherst: Info for students interested in engineering . When I was a student, there also was a combined program with MIT and CalTech, in addition to Dartmouth. I imagine that you may be able to customise your own combined degree program with those or another specific institution that may have specific programs in your area of engineering interest eg., Carnegie-Mellon, UC Berkeley, etc, but you will need to check ahead of time. Otherwise, try to find out whether you can meet their requirements in the 5 College area and apply for their Masters Program. I agree with the link below that pursuing a combined engineering degree at Amherst is not the most time-efficient way to get your degree. On the other hand, if you choose such a program, you will have some advantages over other engineers-you can think across many disciplines, communicate with others who are not tech people, and write effectively among other soft skills. I think those are valuable yet intangible assets that will help you become successful in your profession and in your personal life.