Since every cancer is different in the markers it displays, I think that is unlikely to happen. It would mean an insane amount of vaccinations and the assumption that they have none to acceptable side effects.
There are a handful of embryonic proteins that are normally expressed during development but are absent in the adult that are particularly promising. One of the hallmarks of cancer is dedifferentiation--losing specific markers and function and looking more and more like a stem cell that can continue to replicate, and these embryonic proteins are known to be reexpressed in many tumors.
That's why CAR-T treatments are considered only in the cases where all other options have been exhausted.