I am looking forward to playing the new chart 3 or chart 4 (soon to be formerly known as the midchart or superchart) so I can open 1NT with any singleton if 4441, 5431 or 6331. For a relay starting at 1NT-2♣, there's room for fifty five hand patterns. My first picks are all the balance or semi-balanced hands with 2-5 in each major: 4 x 4333, 12 x 4432, 12 x 5332, 12 x 5422. That's 40. 6322 with a six card minor is another 6.
For the hands with a singleton, I have room for 9, but my intuition is that opening with a singleton major is a recipe for playing 2 of a major in a 5-1 fit. We have to wait for data to see if my intuition is any good once the new chart takes effect. Fortunately, there are still plenty of minor singleton hands to choose from that qualify for the new natural NT: 4 x (54)(31), 2 x 4=4=(41), and 2 x 3=3(61) are my picks (and one free space for Elijah the Prophet). I leave out (53)(41) because I like to open those in the major.
My intuition is that adding these 8 hands with a short minor will be a net plus. It puts the Flannery 4-5s at 1NT. All the 6-card minor hands that are not 6-4 or a singleton major are opened at 1NT. These make it more difficult for the defense to compete. Given that a major lead is usually favored when the NT side is not playing in a major, this will make that work out for the defense less often. Again, data will reveal all in due course. So the full disclosure if asked is natural, 2-5M, not 5-3 in the majors either way with a singleton.
Next, the relay...
1NT-2♣ = game forcing, artificial
2♦ = equal shortest suit (the only hands with a 4+card major in this branch are 4333 or 5422)
2♥ = 5+♠ or 5+m only one shortest suit
2♠ = 4432 1st 6 numerically or 3=3=4=3 denies 4♠ (+1 free spot) rebid in order of frequency, then break the tie numerically
2NT = 4432 next 5 numerically (all have 4♠)
3♣ = 4=4=3=2 or 4=4=(14)
3♦ = 4=5=(13)
3♥+ = 5♥(233) zoom numerically to show the exact pattern
1NT-2♣; 2♦-2♥; ?
2♠ = 5422 one major
2NT = 6♣(223) or (34)=3=3
3♣ = 2=2-(45) or 3=3=3=4
3♦ = (45)=2=2
3♥+ = 6♦(223) zoom numerically to show the exact pattern
1NT-2♣; 2♥-2♠; ?
2N = 5♠ rebid 3♦= 5=4(13), 3♥+ = 5♠(233)
3♣ = 5♣(233)
3♦ = 3=3=(16)
3H+ = 5♦(233) zoom numerically to show the exact pattern
1NT-2♣; 2♠-2NT; ?
3♣ = 3=3=4=3, 2=3=4=4, or 3=2=4=4, rebid in this order (i.e. highest frequency hand pattern lowest, then break ties for equally likely hands numerically)
3♦ = 2=4=3=4 or 2=4=4=3
3♥+ = 3=4=2=4, 3=4=4=2 or I forgot this space was empty
When I say numerically, I mean write the pattern as a 4-digit number and the lowest bid corresponds to the lowest number(s).
The first branch is whether a hand has more than one suit that has the shortest length or not. (E.g., 4=3=3=3 has 3, 5=4=3=1 has 1.) But since there are 22 like that and 32 not like that, I throw in 3=3=4=3 with the single shortest suit hands.
The system is a bit transfer oriented so the described hand can be dummy more of the time. This works best with a low-strength NT so the strong hand is being led up to also. Of course, the NT opener is already declaring NT so that horse has left the barn.
With any luck, you can see this in action at the 2018 US team trials.
Plus... it's free!