Sorry what's a derived key. Not sure your question makes sense.

You can hash any input of bits and use that as a key, whether the bits are words or not.

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Basically I'm trying to do BIP-32 but start from a keypair instead of a seed. In order to make it work across multiple clients I'd need to have some sort of standard way of coming up with a chaincode when you're not deriving that from the seed directly.

Not sure I understand all of this: https://github.com/bitcoin/bips/blob/master/bip-0032.mediawiki#user-content-Specification_Key_derivation

But like I said "deriving" a key usually means computing a hash on some string of bits and then just use that as the private key more or less directly. In BIP 32 the input bits are just the private (parent) key.