Lets look at that Kaplanville and Fantoni-Nunes mix from a 1S opening.

If 2S is a Fantoni-Nunes type bid, covering 10-13 with 6Ss or 5Ss with shape (but not including 4Hs), then opener's two level rebids to a forcing notrump change. With a 5-4-3-1 with 3Hs one should open 1S to find a 5-3 H fit, and if 5=1=4=3/5=1=3=4 then open 2S to try to block a H overcall.

So 1S-1NT--?
2C: With a four card or longer minor, if less than 17 exactly 4 in minor and 5S and if less than 13/14 will have 2 or 3 Hs (this rebid will also include 5-3-3-2s if you open 1S with them and don't pass 1NT)
2D: 5+Ss, 4+Hs, up to 14, or 17/18+
2H: 6+Ss, 13/14+
2S: 5+S, 4Hs, 14/15-17
3m: 14-16, 5-5+
3H: 14/15-17, 5-5+

After 1S-1NT--2C-?

2D: Positive, Game Force opposite 17+
2H: 5+Hs, up to 9
2S: 2+Ss, up to poor 8, or singleton S and no good bid up to poor 8
2NT: Both minors, up to poor 8 Or 6+Ds 8+ (will bid again over 3m by opener)
3C/D: Long minor, up to poor 8

After 1S-1NT--2C-2D--?

2H: 10-13, 5Ss, 2-3Hs
2S: 13/14-16, 5S, 4 in a minor. 3D is now a forcing ask.
2NT+: 17+