This is a small study of a third dose of the AZ vaccine (75 people), given almost a year after the first shot. They are looking at both the increase in immune markers and reactions to the third shot compared to the first two.
They found that systemic reactions (flu-like symptoms) were less with the third shot as compared to the first two. AZ is adenovirus-vectored, so the antibodies to the vector would be expected to reduce the amount of vector that gets through. We can't assume that the RNA vaccines will be the same, as the second dose of those is typically worse, which is not true of AZ. But most likely the J&J vaccine would be similar to AZ.
Localized reactions (sore arm / redness) were about the same for the third shot as the earlier ones.
There were nowhere near enough people in the study to see any of those rare autoimmune reactions. That is something that would require hundreds of thousands of doses to show up.
Immunity did increase after the third dose. Antibody levels a month after the third dose were about double the levels a month after the second dose. Between the second and third dose, they had declined, but were still on average higher than the peak after a single dose. So immunity is holding up reasonably well, but a booster also does improve antibody levels to an extent that would be expected to give increased efficacy.
They also looked at T-cell numbers. T-cell levels decayed over time, and after the third dose were boosted a bit. T-cells were definitely less "boostable" than antibodies in this study, as their levels after the third shot were a bit lower than after the second shot.
In many parts of the world, the AZ vaccine is the only one available, so this will be valuable information for them. But if you live somewhere with access to multiple vaccines, you will get a larger boost from mixing vaccines rather than using AZ three times.
Link to study: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3873839