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The standard process for reading and writing the GATT database maxes out at 22 bytes.
Take a look at the long_characteristic example in SDK 2.X
This sample application demonstrates how to read and write values to a characteristic value larger than 512 octets in length.
You will find this thread helpful as well: Support for very large characteristics
I should have been more specific, I'm writing from a BCM20737S in a central role to another BCM20737S in a peripheral role. The long characteristic example only explains the server/peripheral side. Fortunately I can reduce the transfer size to 22 Bytes.