Can this treatment be designed to target the mutations? ( So you didn't lose healthy cells ) I'm assuming the mutations present on the cell surface as well, but I am unsure.
In that case, would any cell that mutated to avoid there treatment, de-cancer itself?
That would be a sort-of holy grail of cancer therapy. The problem is that the best equipment to develop a high-affinity antibody, or find the correct T cell receptor to the mutation is the patient's immune system - and they've already done it.
Predicting what sort of antibody or T cell receptor will bind a specific mutation (more technically a piece of protein with the mutation in it - about 10 amino acids long) is hugely difficult - it requires a very good understanding of how all the amino acids fold and interact in a 3D spatial model, and we simply aren't there yet.
Your last question really depends on the mutations. Further mutations would stimulate more of an immune response, but a mutation could, for example, increase the ways a tumour cell hides from the immune system. On the other hand, it would be hard for the tumour cells to de-mutate itself to avoid TILs already specific for that mutation.
In that case, would any cell that mutated to avoid there treatment, de-cancer itself?