Can you tag up in softball?

Yes, if it's caught for an out. I saw Jose Canseco make a smart play once (which surprised me because he was usually pretty dumb.) Score tied in the bottom of the ninth, one out and a runner on third, Canseco was playing right field. There was a long fly ball hit towards him, and he let it drop foul rather than catch it for the out--because the runner on third would have tagged up and scored the winning run.