Well as some of you might imagine, it's been hard for me to stay out of this thread as long as I have!

In case anyone is interested in my background on this subject, I have 2 careers going simultaneously.
I have been a professional trumpet player for 20 years, and a mouthpiece maker for 15 years.
And guess what my mouthpiece specialty is?
Threading interchangeable rims, cups, and backbores. I have done many letters, brochures, and clinics on the subject, but will try to keep it brief here.

Can you imagine if mutes were permanently attached to the instrument, and every time you needed one you had to put down your "open horn", and pick up your "straight mute horn", or your "cup mute horn"?
What if each horn also had the mouthpiece permanently attached, so if you wanted to go from a 7C to trying a 3C, you would have to get all new horns (one with each mute) that had a 3C attached?
How about if the tuning slide couldn't be varied, and if you were sharp, you had to pick up a "flatter" horn, instead of just adjusting your slide?  Sounds pretty ridiculous, doesn't it?

If you talk to someone that has developed a good understanding of mouthpiece components, and used them to their benefit, they most likely will feel that going back to a one-piece mouthpiece is about as limiting as the suggestions in the previous paragraph. To have options, or not to have options; that is the question. The idea, of course, is NOT to switch components at will for no good reason, but only for good reason. This is where many players get lost: when to switch, and for what good reason?

Thank you to the several TPINers that have already described their uses. We are all different, not just in what mouthpieces we use, but also in how much switching we can take before it has a detrimental effect. Personally, I can't switch much of anything before I start to feel my playing efficiency going to pot. If I don't have a natural-feeling fine-tuned taste for the equipment, I start wasting a lot of energy, and my tone, pitch, endurance, range, finesse, and musicianship in general start to suffer.
I am best off when I warm up on the piece that I need that day, and don't even try another. It's usually the same piece every day.

In my shop I have just about every rim, cup, and backbore from Bach, Parke, Reeves, Schilke, and Warburton, with a sprinkling of sizes from Giardinelli, Stork, Black^Hill, Tottle, Bush, Sanders, Jet-Tone, Benge, Parduba, Rudy Muck, Bukur, Marcinkiewicz, Purviance, Wick, Reinhardt, Yamaha, Holton, Minick, Conn, Besson, Perantucci, King, Monette, Costello, McCann, Colin, Kanstul, --- well you get the idea.
It's well over 1 million possible combinations.
Fortunately, I've never even been tempted to try them all, or I'd be in a straight jacket for sure.

Since I've been making mouthpieces, I've been trying them less, because I just get what I need. The frenzy comes when you CAN'T get what you need.

During my decade in NYC, I learned a lot about matching other players. Even for the same style of music, I don't always play with the same sound. Sound can be real personal.
I play differently next to John Frosk than I do with Dave Stahl. We all play Lead Trumpet, but only those who adapt musically also get called for section work.
This can, at times, be better accomplished with a change in backbore, or even cup, but that's not always necessary. Whenever possible, I try to accomplish the changes in musical personality without changing equipment. When a change is necessary, I swap out only the component(s) that I need to, and keep the rest (rim at least) the same.

For those who have not seen it, the following web page may help:
http://parke.net/mpc/evaluate.txt

Well, I guess I've babbled on enough for now.
There are other mouthpiece makers, besides me, who also do threading work. Bob Reeves, Scott Laskey, Terry Warburton, John Stork, Greg Black, Joe Marcinkiewicz, etc.
They are all my friends, so I can't comment about the relative quality. But I will encourage anyone who is serious about quality to get yourself a good set of measuring calipers, and learn to use them accurately.
Ask lots of questions, and insist on common sense answers, not hocus-pocus. Talk to professionals players in the particular field you are pursuing. Know the difference between a paid endorsement and a personal recommendation.

Please feel free to call Dianne & me if we may be of service.

Best Wishes,
Jeff Parke
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Jeff & Dianne Parke
1315 N Tustin Av
# 354
Orange, CA  92867
(714) 288-0902
jeff@parke.net
http://parke.net