Open Twitter, allow anyone to be a Twitter server, and sell their services to Twitter providers who don't want to deal with Twitter nuts and bolts, as Disqus does for comments and Google does for gapps.
Be an expert in Twitter and sell training to implementers and users, as GitHub does for git.
Have free and paid levels, as GitHub, Disqus, Dropbox and countless others do.
Have all paid services, as old school businesses do.
There's probably more else that I haven't covered.
Why joke, merchandising is good business. Look at the Star Wars franchise, over 30 years it's earned an estimated $22B of which $6.68B was generated at the box office. The largest chunk comes from merchandise ($9B). [1]
Granted, kiddies might be less interested in a plush fail whale than a plastic light saber.
Why, the Twitter service itself. Its called lock-in.
Rewrite the licensing to say for non-commercial use only, except under special license. Allow businesses to opt into a licensing agreement for a few hundred bucks a year. Release the hounds on any unlicensed companies.
Remember that Twitter has a certain 'scale' in terms of expenses (employees, servers, etc) and in terms of VC invested so far. So bussiness models that generate less revenue than required by this scale are not acceptable to them (their investors).
Couple of ideas: I'd love to filter out people who I normally like to follow but suddenly have decided to tweet copiously about some mundane sporting event. And I'd pay for a way to block people who spam my favorite hash tags.