If I were to create a 2-of-4 multi-sig wallet using the 3 seed phrases of an existing 2-of-3 wallet, plus a new seed phrase that I instantly destroy, would I then effectively have a new completely independent 2-of-3 (technically 2-of-4) multi-sig wallet that uses the same seed phrases as the existing wallet?
You would have to transfer any funds from the 2-of-3 multisig address to the 2-of-4 multisig address on the blockchain. But yes you could do this. I don't know why you would do this! Assuming the 2-of-3 can be spent using 2 of the 3 private keys (A, B and C) the 2-of-4 can also be spent using 2 of the 3 private keys because you threw away the fourth. Maybe to obfuscate the fact you are using a 2-of-3 on the blockchain? The potential benefits of doing this are minimal if not zero.