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.
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.