Amex denied me today... twice!

Well okay maybe only once. I applied for the old Amex Blue Cash, and the application says "cancelled" because I have a BCE. Bummer.

Also applied for the platinum (before the blue), got the pending message, called in, and rep says it was denied and I will get an email/letter saying why. He said that I can call in to repeal if I wanted to after getting the denial letter. I guess the reason for denial is too many recent inquiries. I opened a PRG biz in Oct, FR in Oct/Nov resulting in my credit limit being lowered to a tenth of what it was before, SPG in Dec (instant approval for $20K) along with other non-Amex cards.

Any recommendations on what I can do to get the Platinum approved? I offered to reallocate some credit line from the SPG and CSR said no. Can I upgrade the PRG biz to Platinum biz?