For those interested, it may be possible still for someone to invent a new mouthpiece design that would be patentable, but if one were to play the odds, it's probably not too likely to happen for the contours of the mouthpiece. Without getting into a treatise on patent law, for something to be patentable, it must be different from what was known before the possible invention (termed the "prior art"), and it must be "non-obvious" to a person of skill in the art (here, presumably the art of designing and/or manufacturing brass instrument mouthpieces) who has knowledge of all that prior art. Additionally, a patent has to be applied for within a given time period (that requirement has many aspects, but the most commonly applicable one is that it must be filed within 1 year from the first public written description of the invention or of the first offering of the invention for sale).
In the late 1800's and early 1900's a number of patents were filed on brass instrument mouthpiece designs (just as they were on valve configurations and other aspects of instrument design). Mouthpieces are a good example of more and more variations being manufactured, and then becoming a part of the prior art that a new design would have to be non-obvious over, in order to be patentable. Most of the common variations we think of, such as cup shape, rim contour, etc. would be considered matters of design choice to a skilled designer, not sufficiently different to be patentable.
For those wanting to see what has been patented in the past, brass mouthpieces are generally classified by the U.S. Patent and Trademark Office (in an arcane classification system) in Class 84, subclasses 398 and 399 (adjustable mothpieces). Here is a link that may work to get you to a search for subclass 398:
http://patft.uspto.gov/netacgi/nph-Pars ... %0A&d=pall
More than anyone wanted to know...