@Sherman: You are misinterpreting the science. Yes, you can TEST POSITIVE for COVID multiple times. I have a family member who tested positive and negative on and off daily for 6 weeks straight (worked in a nursing home).
However unless biology is completely wrong, you cannot get infected with SARS-CoV-2 and develop COVID-19 after you've already obtained SARS-CoV-2 and went through the entire COVID-19 lifecycle.
The case studies and news articles you point to are about people testing positive multiple times, or getting sick, getting better and relapsing, or people that tested negative while being on treatment and then test positive again. That isn't completely unsurprising given the replication levels during testing give you orders of magnitude higher chance at false positive than they should be. There are also a margin where you can test and get false negatives. In most cases these relapses were in EU, Brazil, Mexico where many testing is done using Chinese-sourced test kits which have ~20% failure rate.
Now the question is whether you have been sick and tested positive, should you get vaccinated:
- I believe yes, as I said, the tests give orders of magnitude too many false positives. It is entirely possible you got a flu or a common cold, tested positive for COVID because you were too close to someone with actual COVID and some remnants of dead virus were in your nasal tract.
- If you have been part of a research study or you got a private COVID testing done, and your COVID-testing was done with blood samples, and that proved positive, then NO, it isn't necessary to get vaccinated. You have immunity, that's what the blood test tests for, whether you have T-cells that attack COVID-19 samples, and if you have immunity, that means you were infected at one point.
This also means, if you have your blood tested after the vaccine, you will test 'positive' for COVID-19 blood testing.
Note: I have been involved in HIV and other immunology research. Again, it is possible, but extremely unlikely that we are collectively wrong about viruses or about COVID-19 in particular. If COVID-19 was a 'designer virus' or mutates extremely quickly it could indeed be possible to get multiple infections, to date, there is no evidence of that, if we had evidence of that, we'd have no vaccine.