Here are interesting mouthpieces from manufacturers like UMI [Conn, King, and Benge] that don't fit their usual designs, plus uncommon examples from other manufacturers.
Here is a unique UMI-Conn example to start:
Type: Cornet mouthpiece
Brand: Conn/King/Benge
Maker: Lausmann
Type №: 7BR ["British" brass-band type]
Type: British-style/modern short shank
Bach equivalent [when available]: Bach № 7 [rim], nearest a 7V [cup type; the 7BR has a deeper, more rounded cup]
Where made: Nauheim, Germany
Dates of manufacture: late 1990s or early 2000s
According to the eBay listing for this mouthpiece, this is an example of a mouthpiece manufactured for shipment with UMI cornets. Most recently, the Conn 34A cornet [the last cornet produced under the Conn banner] usually shipped with a 7C mouthpiece. The King 2220 Legend cornet comes with a "King British-style #7 mouthpiece", which is this model marked "King 7BR" on a different outside blank. Based on the fact that this is a deep, U-shaped cup, I would imagine that this mouthpiece is similar to a Bach-type 7V with a rounded-V cup [the closest Bach is the V-cup 5V, the U-cup 7A a far second]. Notice that this has a short shank to compensate for the deep cup--something almost unheard-of for standard Bach and Conn mouthpieces. The only other short-shank Conn mouthpieces were proprietary ones made pre-1957 for cornets, with a different taper and length that would make them less usable in modern cornets. This first appeared as the "7BR" cornet mouthpiece listed on the old UMI website ["BR" presumably standing for "British"].
Another mouthpiece not often seen is the 5½SC, a UMI product under the UMI, Conn, and Benge banners.
Type: Cornet mouthpiece
Brand: Benge [this example]
Maker: Lausmann
Type №: 5½SC [shallow cup]
Type: standard cornet
Bach equivalent [when available]: Bach ~№ 5½
Where made: Nauheim, Germany [this one came in a sealed bag with a sticker stating "Made in W.-Germany"]
Dates of manufacture: 1990-early 2000s
Mentioned in this UMI mouthpiece publication, I have yet to see a UMI version of the above mouthpiece, but, as you can see, the Benge version does exist, and I have seen a few Conn examples, too. There is also a similar model, the 4SC, of which I have a trumpet version [also Benge].
Who says they only made circular mouthpiece cups?
Type: Cornet [?] mouthpiece
Brand: Cauffman
Maker: J. W. Cauffman Co.
Size №: 1K
Type: Asymmetric/standard cornet shank
Bach equivalent [when available]: none
Where made: U. S. A.
Dates of manufacture: 1940s?
Not the only asymmetric mouthpiece out there, but this is an earlier example.