Phrases like “sit down” and “stood up” have redundancy built in. Down is the only direction one can sit (unless you’re in space) and there is no other way to stand except up. However, Jill can sit next to Jack, but she’s more likely to tumble after him.
Amendment: There is one exception where the directional word becomes vital: if you have a position of authority you can stand down or be stood down. (Thanks to J.L. O’Rourke from Millwheel Press for reminding me of this fact.)
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