One of the city’s oldest budget hotels is being modernized and might expand. Owners of the 125-room Cosmopolitan Hotel in Tribeca are adding a roof deck to the seven-story, 165-year-old building and a new entrance. The owners are also trying to build a six-story addition to the hotel, at 95 West Broadway at Chambers Street, next door. The modern addition, which is opposed by Community Board 1, would be red brick with an all-glass storefront. It would replace a two-story structure that now houses a Mexican restaurant. The hotel owners need approval from the Landmarks Preservation Commission to move forward with the plan since the hotel sits in the Tribeca South Historic District.