[edit] Apparently, I'm wrong, "utility" is an explicit requirement. But let me tell you, nobody ever asked me to justify the utility, not even a little bit. I think it's just assumed that if you're willing to pay the patent fees, it's likely to have some utility.

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AFAIK there's isn't. You can patent a leash for rodents, and PTO is not going to say "it's not acceptable, nobody wants to put rodents on a leash". The only questions are whether your invention is novel and non-obvious, not whether it's useful.

As such, if you can patent stage A that produces <unuseful stuff B>, nobody will tell you that it's unacceptable because B isn't useful. The usefulness is a completely separate question, to be decided by the market.

A company could do that, but what advantage is there to doing that over simply keeping stage A a secret? By patenting stage A, you are awarded a temporary monopoly over stage A but also giving competitors a head start to reverse engineer stage B. By not patenting stage A, you don't get the temporary monopoly, but you also don't publicize anything about stage A that would give competitors the head start on stage B. So it's the same tradeoff that always exists with patents.

Stage A must be provably useful, provably non-obvious, and provably new.