I just realized I don't get the sentence that says "you can start up to 3 simultaneous bounties". I have picked one answer that gave me the best insight to my question and then agreed with aCVn to award bounties to other answers that I found overall useful in that they address slightly different aspects of the problem.
Now I have one bounty and no way to do a three-way split (or even a two-way, for that matter). Funny enough, I can't even start a second bounty on the same question.
Did I miss some important step, or is that how the system works?
Also, I imagine it is bad manners (or, in the least, unheard of) to ask the recipient of my bounty to start their own bounty to be awarded to another answer.