OP, different banks are known to be more liberal than others when it comes to CLI's.
In my experience, Credit Unions are the way to go. (Though an Amex Green is nice to have as well as a prev poster mentioned).
If you have any military connection, NFCU and PenFed are both great and very easy to get large credit lines on assuming you have solid fico scores.
After those 2, the next would be Alliant. You can join the national PTA for $20 to qualify for Alliant memership. Each major milestone in my credit was had from a CU: My first $10k card, my first $25k card, my first $50k total line of credit (between a reolving line and credit card at NFCU).
Open an account. Move assets into it. Call or go into a branch (if possible) and talk to a loan officer or credit analyst.
If you want to go to a traditional bank, Amex is great for large guidelines/limits but they will probably Financial Review (FR) you if you want really large limits. That means signing a release allowing amex to requerst past tax returns from the gov't. If you're unwilling to do this, don't get an amex. At any moment they could decide to FR you and if that's the card you're running your business on it could cause you misery. At the very least, have a good backup.