I have thought about earning a second LLM. I would be motivated by a desire to focus on different subjects and to get a degree from a more prestigious school.
LLMs are very specialized degrees and typically the people pursuing one knows what type of law they want to practice (many/most LLM programs require you to have at least two years of experience practicing law). I believe the most common LLMs are for tax law, patent law and programs for foreign attorneys who want to practice law in the states. If you're area of specialty is tax law you would do an LLM in that area. Unless you're wanting to change career paths I can't see how/why someone would pursue a second LLM.