…So, if a player happens to be holding two or even three Secrets, they have to reveal all of them – and take multiple penalties?

A: Yup: “Secrets” plural; “play them immediately.”

It’s pretty punishing, but if one of your Secrets was that you were the Murderer, then it kind of makes the other two moot. If you’ve been eliminated, then who cares if you just lost your hand and half your Keepers?

By the time you’re able to jump back in (presumably after your jail time), your reputation as a Sandwich Thief and/or Statuette Counterfeiter is going to be long since forgotten, overwhelmed by the scandal of your greater crime.

All this is to say that you can’t be retroactively punished for any other Secret/s you may have had before your elimination. This still makes sense, even in a two-player game, where you jump back in without delay.

So the only time you’d really be doubly punished is if you have Sandwich Thief! and The Statuette Is a Fake! which is pretty annoying, but at least you’re still in the game!