We can convert even to (p ^ 2) for secp256k1 but this is useless because we cannot do twist/subgroup/invalid curve attack.
Could you please explain what do you mean by p^2 exactly?
This is very easy to do but we cannot do attack because we got infinity zero points if we can do birational mapping for two or more curves using main curve secp256k1 we can easily compute private key of public key.