Do you have a business card now? Have you tried to call your current cards and see how high they can raise the CL (but not actually raising it)? That may be the limit your new card will be willing to go.

If it's the same bank of your other cards, lowering the CL on other cards will also help.

Of all the cards I have, Chase cards seem to have higher CL. I have to call Chase to lower them each time. Coincidentally, I also have accounts with them.