ST. PAUL, Minn. — The McGough general contracting company has been hired by Winona State University to design a 340-bed dorm and shepherd the plan through a maze of approvals. A McGough spokesperson described the proposal as a “state-of-the-art residence hall.” As plans now stand, the dorm would be a five-story structure on the southeast corner of the main campus – on Main Streets and bounded by Mark Street, the Canadian Pacific mainline, and the university’s power plant. At 71 feet, the dorm would be the second tallest structure at Winona State — after 1he 13-story sky-scraping Sheehan Hall. The height would require a city zoning variance.