I've done Tunlock three times in a row now. No new message the third time.
Now I'm using Rbuff.
Nothing unusual the first 11 times. (erm, take with grain of salt, I may well have missed the message below for #11 if it did appear, as I wasn't paying enough attention.
12th-15th times, as I believe you've already seen, Wyrd,
"You haul on the puzzle with all your might. For a second before you black out, you think you can hear tendons ripping.
When you come too, you feel better rather than worse. Either way, you're pretty sure that was more difficult than last time."
(but still got 10 energy of buff)
After 15 uses, the option no longer appears! It appears that each unlock allows 5 additional uses of the buff, and you get a different message 'warning' you that it's going to run out soon starting on the 4th-to-last use.
.
.
.
Note that Wyrd has been spading the same thing after one use of Tunlock, and has found something interesting. Hopefully together we should soon get a good idea of what multi-unlocking really does.
In the beginning, men were mortal.