Authenticated encryption using asymmetric keys
You will always need at least to blocks (=512 bytes in your case) if you want to encrypt and sign some data.
Any RSA signature block, be it armored with PKCS#1 v1.5 or PSS (or even textbook RSA) will have the size of the modulus (256 byte), since it is the output of a RSA operation. So if you want to add some plain text data to that, you will automatically need to start a new block.

All said is under the assumption of using two keys of equal size (2048 bit), as you suggested. You could get away with one block if your signature key has a smaller bitsize (e.g. 2048) then the encryption key (e.g. 4096).