I thought that double blind referred to "the subjects" and "everyone else." If not, then we could have 5- or 6-blind experiments, too.
I suppose in theory we could -- but the point is not to rack the numbers as high as we can, but to identify and eliminate sources of bias.
Triple-blinding covers yet another source of bias that traditional double-blinding doesn't. In a typical double-blind experiment, I as the experimentor know which group (red pill or blue pill, group A or group Bl) a subject belongs to, but not whether the placebo is red or blue.
However, I might be able to make a guess about which is which. There have been a number of cases where a double-blind study has been stopped midway through on ethical reasons, because it's so obvious that group A is getting an effective treatment and group B is the control that it becomes unethical to withhold treatment from group B. That's an extreme example, but it does show that merely not
formally knowing which pill is which doesn't accomplish total blinding.
The problem is in cases that are less clear-cut. Suppose, for example, that I'm testing a particular drug, and one of the patients in group A (whichever that is) starts showing signs of a serious side effect --
grossly elevated blood pressure, or something like that. Something serious enough to warrant closer monitoring of all of group A in case it's caused by the drug. But if I start monitoring group A (but not group B), then I'm no longer giving both groups the same treatment --the "placebo" isn't. But if I start monitoring both group A and B, knowing that group A is the group that I consider "at risk," then I'm likely to start biasing the results. Someone from group B comes in with a marginally elevated blood pressure, and I might not take it as seriously as if someone from group A comes in with the exact same numbers.
So my mere knowledge of which group they're in is going to bias my interpretation of the clinical presentation. This could also apply to something as simple as evaluating the effectiveness of a new pain-killer. If the first three patients I interview from group A tell me that this new pain pill is the greatest thing since the invention of beer, I might come to
expect that group A will report improved performance, and start mentally upgrading the effectiveness of reports from that group.
So a fairer and less biased way of doing this is to let someone else do the monitoring, someone who knows that the patients are involved in an experiment, but not which specific group they're in. So this way, I can say "I want you to monitor all sixty patients for blood pressure," and they'll get the same treatment regardless of the color of the pill they get, and I can tabulate the results this third physician got later as another, independently blinded, study of the effect of this drug on b.p.
If you can figure out yet another source of bias that isn't covered in this triply-blinded study, then by all means, propose another protocol extension. Write it up for the JAMA, if you need to. The whole point of these kind of trials is to minimize bias anyway.... and if it takes ten separate physicians to run an experment "properly," then that just means more co-authorship opportunities.