When I was in Los Angeles recently, I also spent some time with a knowledgeable contact in the cloth trade and learned about a couple of fantastic new books by William Halstead, a weaver and mill based in Bradford, Yorkshire. Operating since 1875, they are perhaps most well-known for their classic English mohairs.
Mohairs are sheared from the Angora goat and have a higher luster than typically found in other worsted fabrics (see the wool-mohair jacket below). The younger the goat, the finer the diameter of the individual hairs (kid mohair). When woven into cloth, mohair provides a nice firmness and memory (or recovery) for retaining shape. Mohair blends make fine cloths for dinner jackets and what I would call "evening suits" (or evening jackets) for events which are not quite black tie and where a business suit may be acceptable but a bit predictable.
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I looked through a couple of new Halstead books of English mohairs and Super 120s worsteds. The former contains wool mohair blends but also contains one cloth of 100% mohair. It's an unusual fabric to be sure, as I don't recall ever seeing a 100% mohair before.
Along with the summer formal shirt idea described below, the English mohairs book would be at the top of my short list for a summerweight dinner jacket cloth. The second Halstead book has lighter weight worsteds in classic solids and terrific patterns, ideal for leisure or business summer suits. These have a softer finish than the Lesser tropicalweight worsteds for instance.