You can. Or more precisely, you can infect it with a virus that mostly just hurts the cancer. This has been done successfully with measles, and is still in the testing phase. Since we should have immunity to measles due to vaccination, the measles primarily hurts the cancer.
[NIH](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3926122/)
Edit: One downside is that our immunity makes it harder to deliver to the cancer. You have to inject it straight into the cancer or take immune suppressors.
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