I strongly discourage second BAs, unless you're switching to, say, engineering or scientific research.
Most second BAs are a waste of money.
Go for a Masters. It will cost less, take less time, and be more valuable in the eyes of employers.
If you're just doing it for fun, no career intended, and money is no object... by all means, get 2... or 22 BAs. Otherwise, go for an MA or PhD or JD or MD or another terminal degree.