I've never seen any GOEs more than +3 and/or less than -3 before.
There haven't been any, and there won't be unless there are significant changes in the rules.
I knew it never had even in the beginning when I took on the argument with let`s talk about it in the other thread. But I just stubbornly think that with the rules listed in the first post of this thread, it can't be unless there is some good logic in mathematical reasoning (I thought it has when I planned to open this thread), or the fact that multiple -3 faults in one jump rarely happens so that it can be ignored.
No, it's not that rare, especially at lower levels. But a lot of those errors can also be penalized other places than the GOE, and elements that have good aspects despite having a mandatory -GOE can be rewarded elsewhere.
So it's not true that an element with one serious error will have the exact same impact on the final score as the same kind of element with multiple errors, even if they both have the exact same GOE.
(edited to add

Working through the example from the other thread.
one guy landed a gorgeous rotated quad and get -3 GOE for the lack of preceeding steps. Another guy has no preceeding steps, underrotates his quad, two footed it and then fall. He gets the same -3 GOE as the first guy. They rule is clear designed for the benefit of a falling guy. Even Chan ubers cannot be so into unfair play.
Correct me if I'm wrong. I think for the first guy, he gets -3 GOEs for lack of required preceding steps. But he gets full credit for his perfect quad jump as well as +3 GOEs for his quad. For the other guy, he gets -3 GOEs for lack of preceding steps. Also he gets UR call, and -3 GOEs for two footed and then fall. No positive GOEs for his quad. He also gets a mandatory -1 deduction for the fall. Sounds like there are big difference between them.
This must be a short program, if the lack of preceding steps is an issue. The type of quad is not specified but I'll assume quad toe loop.
Gorgeous quad with no preceding steps:
A judge can start with +1, +2, or +3 for what the jump would deserve in a long program if it meets two, four, or all six of the following bullet points:
2) varied position in the air / delay in rotation
3) good height and distance
4) good extension on landing / creative exit
5) good flow from entry to exit
7) effortless throughout
8) element matched to the musical structure
[bullet point 1) unexpected/creative/difficult entry would not be true if there are no preceding moves, and bullet point 6) good unison and close to each other in all phases would only apply to pairs]
Then the judge must
reduce the GOE by three grades, i.e., subtract 3 from whatever positive grade she started at, and the final GOE must be negative. So if the judge thought that gorgeous quad was worth +2 or +3 under long program rules, the final GOE would be -1; if she thought it was only worth +1 to start with, the final GOE would be -2. If it's gorgeous, presumably the judge would not start at 0, so the final GOE that the judge keys into the system would not be -3.
You'd only see a -1 or -2 in the protocol for that element in that judge's column. You would not see the +2 and -3 in the judge's thinking that balanced out to -1. Let's assume for easy math that all judges give -1, although in reality some might give -2.
So, under the Technical Elements score, that element gets the base value of a quad toe (10.3) with -1 GOE (subtract 1.0). He ends up with 9.3 points for that element.
Judges may not explicitly consider that element in determining their program component marks. But it's likely that, at least on a subconscious level, the lack of preceding steps would have a negative effect on the Transitions score and the gorgeousness would have a positive effect on the Performance/Execution score, and maybe a bit on Skating Skills (and Choreography and/or Interpretation if it deserved the matched to musical structure" bullet). So let's say it adds 0.25 to the PCS total after all the judges component scores are averaged.
Final contribution of that quad to this skater's short program score: 9.3 for the element + extra 0.25 in PCS = 9.55
Now, suppose that this jump needed to be a combination and wasn't (i.e., there were two non-axel jumps in the program and neither of them had a second jump as a combination, and there was reason to believe that the other one was supposed to count as the jump out of steps), so the final GOE is required to be -3 (because of the lack of combination, not because of the lack of steps) regardless of how gorgeous the jump was.
10.3 - 3.0 = 7.3, + ~0.25 in PCS = ~7.55 final score
No preceeding steps, underrotates his quad, two footed it and then fall
The quad is underrotated -- I'll take this to mean between 90 and 180 degrees since it doesn't say "downgraded" -- so the base mark for the element is only 7.2 to begin with.
Any one or two of the errors mentioned would require -3 GOE, and that will be subtracted from 0, not from a positive number, because it's not possible for an element with all those errors to meet at least two of the positive bullet points. So the final GOE for this badly flawed quad attempt will be -3 from all the judges, since that's the lowest possible GOE.
The total contribution of this element to the Total Elements Score is 7.2 - 3.0 = 4.2.
It also requires a fall deduction of 1.0.
And let's say the extreme messiness of the execution, along with the lack of preceding steps, leads to an average of 0.5 lower total PCS than that panel would have awarded had the jump been successful.
4.2 for the element - 1.0 for the fall - 0.5 for the loss in PCS = 2.8 net total contribution of this element to the overall program score
9.55 vs. 2.8 is a pretty significant difference in how much value the first skater got out of this jump compared to the second.
Even if the first guy's jump was in the combination slot and they both end up with the same -3 GOE, 7.55 vs. 2.8 is still significant.
And even if we ignore the PCS effect since that's subjective and often not conscious so all we can do is guess and estimate, we still end up with a difference of 7.3 for the gorgeous quad with -3 GOE vs. 3.2 for the underrotated fallen quad with -3 GOE and fall deduction.
The GOE is the same but the final effect on the total score is very different, because of points the second guy lost in base value and fall deduction (built in to the system), and probably in PCS as well.