A double major at MSOE would be very difficult, especially if you wanted to graduate in the normal 4-5 years. The CAECM (Civil, Architectural, and Construction Management) Department offers both construction management as a separate major or Civil engineering as a major with a construction management specialty. Other specialties within civil include: structural, water resources and environmental. Architectural specialties include: structural, electrical, and mechanical systems. If Civil Engineering interests you, I myself as a current Civil Engineering student here would highly recommend you try to get into this program instead. Here is a link to more information. http://www.msoe.edu/community/academics/engineering/page/1188/civil-engineering-overview
I've also included your admission counselor in this discussion, Elle Meinholz, if this is an option you might want to consider. Feel free to ask either one of us any questions you might have, hope this helps!
We have a formal track with the CM and AE double major, that is very popular option in our department (5 years for both degrees). If you are interested in doing building construction (commercial buildings, industrial buildings, etc) then that is probably the best fit. If you are more interested in doing highway construction or building dams, bridges, treatment facilities, then the Civil degree with the CM specialty is the better fit. Feel free to message me or post here if you have more questions!