Let me elaborate: Say we have two distinct inputs: $A$ and $B$. We also have some arbitrary deterministic mutation protocol $M$ (for example reversing the characters and performing a Caesar cipher).
Say by chance (I understand this is extremely unlikely) $A$ and $B$ result in the same hash when run through SHA-256. However, when $A$ and $B$ are mutated with $M$ first, and then run through SHA-256, they have different hashes.
Am I correct in this thinking? Deterministic mutations would allow us to have multiple hashes for a single input which would make the probability for collisions even lower, because another input would have to have the same hashes for all mutations.