The 24-year old won 10m synchro silver with partner Sarah Barrow and then claimed another podium place with a bronze in the 10m platform.
Couch won her semi with a 325.30 score, which she improved in the final to 336.20, to edge the final medal place.
But the British champion and two-time Olympian did it the hard way, saving her best dive until last to move from fourth to third as China's Si Yajie took gold and Mexico's Alejandra Orozco claimed silver.
Nick Robinson-Baker and Chris Mears capped off a successful meet for British divers as they also won their second successive World Series medal in the 3m synchro.
Having landed bronze at the previous leg, the Brits scored their highest total since London 2012 to repeat the result behind Mexico's Yahel Castillo and Daniel Islas and China's Li Shixin and He Chao.
Mears also reached the individual 3m springboard final, finishing sixth while Rebecca Gallantree was sixth in the women's 3m springboard final.