Without doing any research on what the actual profitability would be, I'll base this on two factors: 1) how much fun it would be to do, and 2) my (probably skewed) perception of what the demand would be. Get this: a theme party planning business and/or party venue with costumes provided.
We all know I love dress-up theme parties. I know many of you do, too. However, those of us who have hosted dress-up theme parties can attest: the dress-up part makes some potential guests a little nervous and even deters some from attending. So how about this: the party planner not only hooks you up with decor and food and music and whatever else normal party planners do but also comes with racks of clothes in varying sizes and tables of accessories that fit the theme. Guests have full access to the goods PLUS advice from the party stylist (best job ever).
I'd start out with a couple themes and add new ones as the company expanded: Old South Plantation Ball, Victorian Era Garden Party, Roaring 20s Speakeasy, Roman Palace Feast, Wild West Saloon, Medieval Festival, 80s House Party, Pirates at Port, Old Hollywood Oscars Night, Masquerade at Versailles...oh the fun possibilities. Perhaps name each theme after a literary work or something ("Gone With the Wind", "The Importance of Being Earnest", "The Great Gatsby", etc.). A lot of the costumes could be used for multiple themes; a plethora of basic mens suits that could be accessorized in a variety of ways would be a necessity.
I originally got the idea thinking about those old timey photo places where anybody off the street can come in and dress up and get their picture taken in costume. Some sort of set for authentic-looking pictures would have to come with each party. And, of course, a small price to actually get a copy of the photo.
Those attending who enjoy putting together costumes themselves are of course welcome to come in their own outfits, though there will probably still be something for them in the dressing room. You may have the perfect dress for the event, but would you care to borrow this brooch or this hat or these gloves for the evening?
I've looked around to see if there are any companies out there that already do this and the only stuff I can really find are either murder mystery places (which I feel are different enough from us to not be much competition) or little girls birthday parties (princess parties, ballerina parties, that sort of thing). No competition either means I'm a genius or it's not a profitable business model. Since this all started with a hypothetical you're-given-a-bunch-of-money situation which will never happen anyway, let's go with the former.