I consulted Alan Truscott's book <The bidding dictionary>. For development after 2NT opening (or similar 2C-2D-2NT) with conventional meaning (he mentioned just these conventions: Puppet Stayman, Rosenkrantz, Ghose and Smolen, probably the most common at the time he wrote it), at page 130 2NT-3C-3H-3S is labelled "X" - No Standard Meaning, but in some cases, possible meaning are suggested. He suggested at note 654 for 3S in above sequence: "Many use this as a slam try, agreeing hearts". As for 2NT-3C-3H-4C, at same page the sequence is labelled as "FG" and shows 8+ points, and a hand containing 4(-)S 3(-)H 4(-)D 5(+)C. I hope it helps just a bit.