The Standard approach is to allow the 2 rebid to
be pretty much anything, but that (in particular in K/S)
forces a rebid by responder and leaves the auction unclear.
(Playing Standard, who is responsible for starting the
search for a 4-4 major suit fit?)
A set of rebids, attributed to Eric Kokish, attempts to handle these problems. They were designed for use along with a weak NT, but work with any NT range. I'll assume 15-17 NTs and others can transpose from there.
1-2
; ?
Responder's major suit rebid is normally a 4-card suit,
but can sometimes be just a stopper; opener is not expected
to go past 3NT. Opener's 2 and 3
deny a four-card
major, but 2
often contains one.