How many cat scans can you do within a year?

No set limit: There is no set limit for medically indicated ct or any other imaging studies. Prudence dictates that any such exams be done as infrequently as appropriate for the reason required.

As few as medically: Necessary. Although there is no limit, cat scans use ionizing radiation which is associated with cancer. The risk of each scan is incredibly low, but not zero, so no one should have a cat scan without very good medical reasons. In contrast, no one should refuse a medically necessary cat scan because of radiation risk - the current medical problem is always more risky than the radiation risk.