As long as you have spare baggage allowance, you remain landside, and you allow sufficient time, you shouldn't have any problems checking an additional bag. You might get a query, but as long as there's time and spare allowance, it ought to be fine. (If you've used your allowance and want to pay to check another bag for only part way, you may have more issues as they may struggle to price it, YMMV)
There's a few times when I've actually done this very thing, almost always involving duty free and an onward domestic flight. What I'll often do is put a rucksack or similar at the top of my suitcase, which is otherwise full, then buy some duty free before boarding my US-bound flight. On arrival, I collect my bag before customs, clear customs, then find a spare bit of space before the re-check counter. Here, I take out the rucksack, take out some clothes that don't mind getting bashed about, and re-pack the suitcase with the duty free safely in the middle. (We have a question on that topic!). I drop the suitcase off. Then, I head over to the counters, show them my boarding pass, and ask to check a small bag. They scan the boarding pass, check the allowance, print a new tag for the rucksack, and away I go.
However, the last time I did this, they gave me a tag for my rucksack, then sent me over to the baggage re-check area to drop it off. This meant queueing up with everyone else, and having the baggage handlers take the piss out of me for wanting to re-check such a small bag...!