There was a time in m life when I played more and encountered a greater variety of systems. With regard to the system over 1NT-X it says, for the opener, "If partner (the responder to the 1NT), passes – you must re-double". This was one of my favorite agreements to run up against. Often third hand had a flat hand with little or no values and we were about to get a good result no matter where they ran to. I played weak NT with someone for a while and once found myself in that situation. Partner opened 1NT, Rho doubled, I passed, opener redoubled, I bid 2C, doubled, then 2D doubled and so on. I miraculously got a good result. The opponents complained that my bidding was misleading because my first bid of 2C was on a three-card suit. I explained that I decided to start with clubs and stop at the first suit that wasn't doubled. It worked. If neither of them doubled my 2H bid that was their choice.
Anyway, I agree. It's fun and interesting to deal with unfamiliar systems.
The 2C opening that you spoke of came up on the last hand of the second set. Everyone vul, imps, I am holding
S: QJ64
H: 85
D: K852
C: KQ9
Rho deals and passes, I pass, Lho opens 2C alerted as either weak with diamonds or a big hand. Partner doubles. Undiscussed but I sure hope that's a club suit, Rho passes, I pass, Lho bids 2D, alerted as the weak D call. Rho passes. Ok, this is an opportunity. I know more about pard's hand than if Lho had opened 2D followed by two passes. Pard has clubs (yes, undiscussed as I said but I hope she does and she does) and presumably some other values since a shaggy club suit is not enough to warrant the X if my Lho has the big hand and I have zip. So, now what? Well I got it wrong. We can make 3C and we can make 2NT but my choice was 3NT, off 1. It might have worked. Some days optimism works, some days we should stick with pessimism.