Rebecca suggests mission creep as the word of the day. She refers us to an article in the Tampa Tribune which uses the term to discuss the changing role of libraries. The Tampa Tribune was against mission creep on fiscal grounds, but there is also a view that it is the hope of libraries. The newspaper refers to a wide range of new functions and suggests that "it becomes clear that the role of libraries has evolved." In fact, libraries have always taken on new roles which have synergies with existing roles - "... computer centers, neighbourhood meeting spots, art galleries, tutoring sites and even homeless centers", the Tampa Tribune suggests.
A related term is scope creep, used to refer to a project rather than an institution. The Wikipedia article suggests that "it is generally considered a negative occurrence to be avoided."
My role as a library manager is to meet the needs of the university. If that means mission creep - or even mission gallop - then that is something we can handle too. I guess if I ask for suggestions for appropriate mission creep for libraries, people may see this as a negative, but I call it thinking about our future. Any ideas?