This sequence formed a BBF question today. My thoughts:
If Responder has spades and diamonds, Opener will bid 3H with diamond support. With spade support, Opener can bid 4H with the Empathetic Splinter holding and a heart-shortness cater (no wasted values in hearts), 4C with the E.S. and a club-shortness cater, or 3S with other hands (followed by cues, Serious 3NT, and LTTC by the serious partner).
If Responder has spades and clubs, Opener can bid 3H as natural, or 3D with club support. Four-bids are the same, but obviously Opener's E.S. is in diamonds, not clubs.
If Responder has 5350/5341 pattern, he bids 3C Puppet, Opener bids 3H with no 4-card+ major (3NT shows five hearts, instead), and Responder bids 3S. This enables 3H to agree diamonds in the discussion above.
If Responder has hearts and clubs, Opener can bid 3D to show club support or 3S as natural. 4D is an E.S. agreeing hearts, catering to diamond shortness. With a spade-shortness E.S., the partnership makes a decision to either bid 4H (this increasing the number of hands where 3H must be bid) or 4C (increasing the number of hands where 3D must be bid). In this specific sequence, the low-level 3D is very appealing, so that I would make 4D the spade E.S.
If Responder has hearts and diamonds, this is the worst situation. The red suits strike again. Anyway, 3541/3550 is very difficult to handle with alternative methods. If you have a tool, like the one I have for the spade-longer variety, then great! I do not usually have that tool (unless I get people to play full "Batchelder Puppet," which I can explain if anyone wants that). So, I give up on spades as a contract and have 3S show diamond support.
This leaves 3H, 4C, 4D, and 4H for showing heart support. I'll use 4C as the club-shortness-catering E.S., for consistency, and 4D as the other-major E.S., again for consistency.
BTW, when four of Responder's minor is not conventional, this is different from the below-3NT support bid. This shows a very slammish hand.
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