My company performs projects where we assess the fitness of a technology for a purpose. Such a project is called Technical Proof of Concept (TPOC). Our staff tends to make it plural as Technical Proof of Concepts. Well, true, if you have more than one project, then you have more than one concept. But you also have more than one proof. I lean towards Technical Proofs of Concepts. Technical Proofs of Concept doesn’t seem right to me.
What say the Teeming Millions?
If you have more than one proof, then it’s Technical Proofs of Concept. More than one concept, Technical Proof of Concepts. More than one of both, Technical Proofs of Concepts.
How many proofs?
How many concepts?
Multiple
Single or multiple, not important or confusing.
Therefore,
Proofs of Concept.
Someone will be along and tell us the word for this, the Frenchies, and Courts Martial.
Technical proofs of concept
Or you can just plural the acronym: TPOCs. A little inconsistent but both are acceptable. In the latter it’s the acronym that’s being made plural and that’s understood. Spelled out, it’s the proofs that are plural.
I’m sure all member in good standings of the SDMB will agree that you need to put a stop to this. It’s not enough for people in your position to complain to their bosses and supervisors, these things should be taken all the way to Board of Directorses if necessary. In fact, you may want to consider contacting your US member of Congresses as well as the Attorney Generals and state House of Representativeses for each state the company operates in. Have your whole family write letter to the editors, including any brother-in-laws and sister-in-laws. Even recruit friend of the families, and have them contact local Chamber of Commerces for you. Sure, the company management may claim that as citizen of the United Stateses, they have the right to free speech, but that’s irrelevant (not least because many other countries have Bill of Rightses, too!) In any event, some things are beyond the boundary of human decencies, error in grammars like this among them!
Of course, once it goes to court, you can expect a fight. They’ll probably file Motion to Dismisses and Writ of Habeas Corpuses and such. But even if you end up going through all the Court of Appealses, in the end you only have to convince five of the Justice of the Supreme Courts. If you win, you’ll all deserve Congressional Medal of Honors! And if you fail, you can always resort to weapon of mass destructions. Just don’t get captured: I’d hate to see your family end up as prisoner of wars.
“Of Concept” is in replacement of the adjective form.
It describes the proofs as a set as well as one proof.
Suppose one was a “concept proof” , concept is as an adjective. So you’d have multiple concept proofs…
So don’t pluralize.
Do the TPOCs represent separate proofs of the same underlying concept, or are they proofs of different concepts? If the first, then you have Technical Proofs of Concept. If the second, you could have Technical Proofs of Concepts.
The whole thing is Vulcan to me.
Well if there are two proofs there are probably at least two concepts (unless the two proofs refer to the same concept, which is unlikely). So, more precisely, if there is a one-to-one correspondence of proof to concept, it is Proof of Concept. If it is one-to-many correspondence, it is Proof of Concepts.
If there are several proofs of the first type above, it is Proofs of Concept. If there are several proofs of the second type, it is Proofs of Concepts. If the two types are mixed together, it is still Proofs of Concepts.
In graduate school, my apparatus required using many instances of an electrical feedthrough. Everyone else formed the plural as feedthroughs, but I took pleasure in being different and calling them feedsthrough. It did not catch on.
The main reason you would used “Technical Proofs of Concept”, (pluralizing proofs), would be to allow dropping the “of concepts”, thus leaving a coherence shorthand “Technical Proofs”.
Are all our proofs based upon our limited view of the universe? Simple math without a physical obect that you are say counting, but even then that is in our heads, and some people see it differently, let alone a mind that is not human.
Just do them one at a time. 
Technialen prooves of conceptiones.
I think you should go directly to the UN Secretary General with your complaint.
“People called Technicals, think of your proofs now”?
Are you performing multiple proofs of the same concept or proving multiple concepts?
I am not the OP, but the procedure is called a “Technical Proof of Concept”. They are proving that the technology is fit for a specific purposes, so the plural would be “technical proofs…”. This applies in all cases, as even with multiple “concept”, each must have a separate proof!
I think overall, though, the name is very idiomatic, and that is may be rare occasion were using an apostrophe to pluralize the phrase would be appropriate*:
[ul]
[li]Technical proof of concept’s[/li][li]TPOC’s[/li][/ul]
*Grammarians everywhere Gasp! Apostrophe - Wikipedia
Gasp! No, no, no!
“Of all the SDMBs in all the towns in all the world, she walks into mine.” Not SDMB’s.
Nor must the Smiths label their mailbox “The Smith’s,” no matter how beautiful the pyrographic calligraphy (or is it calligraphic pyrography?)
So saith The Chicago Manual of Style, and who are we to argue? There are a couple of exceptions, as noted here.
“Technical Proofs of Concept” (assuming you’re dealing with multiple proofs, not a single proof with multiple concepts), as this columnist demonstrates. The plural goes on the head of the phrase, even if it’s not the last word in it.