Clark is a great University. They do not offer an Engineering major on campus. Like many Universities, they do have a 3/2 program with Columbia. After 5 years you would have two Bachelor degrees in different subjects. Like the “articulation” agreement programs you should read the program specifics carefully. See Clark’s at https://www2.clarku.edu/departments/physics/engineering/index.cfm.
In the same city, The College of the Holy Cross also has a 3/2 program with Columbia. Holy Cross meets the full demonstrated financial needs for all admitted students, See https://www.holycross.edu/academics/programs/3-2-program-engineering.
It is possible that you may be underestimating the quality of the non-engineering minors at some of the traditional STEM universities. Many are not the narrow technical programs of 30 plus years ago. Check out their faculties and offerings in minors. You still need to have the selection and flexibility to put together the subjects you want to study in an ABET program. A university may have very large departments in the non-engineering majors, but you need the flexibility to fit them into your engineering program. Not all of them are flexible. On the flip side, some of the more general Universities are still limited in their engineering offerings.
To make my point, the quality of the Humanities courses at MIT surpass those at many highly regarded non-STEM Universities. It is pretty complicated, but the administrative structure can get in the way of your program design. This happens in many larger universities where Engineering is actually a separate “college” within the university. Don’t assume you can select the courses you want because they are available somewhere on campus.