How can you patent something that has already been patent but the patent has run out?

Answer:
Short answer, you can't. Not in the US, anyway.

Trying to "re-patent" an item that once had a patent would likely end in a denied application. For one, the invention would no longer meet the Novelty Requirement of the patent process - it is no longer "new" or "different," and obviously has been known to the market for over a year (at least 20 at this point, actually). Even if your version were a new size or slightly different material, it still may not pass muster on the Non-Obviousness Requirement.

Patents exist as an incentive to innovation, offering the original inventor (or his assignees) an exclusive period of time to market, produce, and sell the invention, thus recouping the cost of R&D and (hopefully) profiting on top of it. Patents are not even renewable by the original holder, much less available for "re-patenting" by someone else who in all likelihood, if they're simply reproducing a product from the published patent claims, did not put the same research effort into the product's development.

That said, if you had an *improvement* or *new version* of an existing now-expired-but-once-patented item, you could follow the same patenting process as any other invention including conducting patent research, checking that you meet the eligibility requirements, filing and keeping up the fees, etc...
First answer by Inventiongeek. Last edit by Inventiongeek. Contributor trust: 15 [recommend contributor recommended]. Question popularity: 0 [recommend question].