If you've already survived cancer, do your chances of survival increase if you relapse or develop cancer in a different part of the body?

Survival. Survival, cure depends on the type of cancer and stage (how advanced) you have. Cure is based on 5 years intervals (or 10). Oncologist follows guidelines for follow up care. I tell my relatives, that we always have to screen for cancers like we do diabetes and cholesterol. Risks for other cancers are higher once you are a cancer pt. We can battle cancer stay optimistic. We can help.
Not likley. If the tumor recurs at the original site or the same tumor presents at an other, site the prognosis is usually not good. If an entirely new cancer develops at a new site, the prognosis will depend on the characterisitic of that tumor. Having two cancers is generally worse than one.