I once got such a letter from Citi and they offered to divide the credit line on an existing account. I didn't really like the allocation they proposed, so I called and had a different amount allocated from a different card and they processed the approval for the new card.

I would imagine other banks might also offer you a similar option in such a situation ("we cannot extend you any more credit at this time, but we can issue a new card with a portion of your existing $x credit line"). Even if the letter does not explicitly say so, you could call and discuss this with a credit analyst.

Reducing credit limits leads to higher utilization, which is a negative score factor, so the strategy of voluntarily reducing credit lines is one to be undertaken with care depending on your FICO score, how much other credit you have available, and your overall credit situation. (Generally the "too much available credit" reason only comes into play for people with a VERY large amount of unused credit, who would tend to have high FICO scores anyway.)