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Becky Downie secured gold on the uneven bars, while her younger sister Ellie claimed silver on the vault and floor.
Becky, 24, pipped Russian world champion Daria Spiridonova to the title by scoring 15.5 points.
Sixteen-year-old Ellie, who scored 14.933, came second to home favourite Giulia Steingruber.
Becky's uneven bars success means she reclaims the title she won in 2014, while Ellie's vault and floor silvers take the GB women's tally to four medals in Switzerland, following Saturday's team silver.
"I'm so pleased not just to win the gold but to do it with my hardest routine," Becky Downie told BBC Sport.
"In my mind I knew I was going to go for it today; I needed to test it - hopefully if I make the team - for Rio."
Ellie finished second to home favourite Steingruber in both her finals.
Last up on floor, the younger Downie performed a routine that pushed her team-mate Claudia Fragapane down to fourth and out of the medals.
"I'm so chuffed with the vault silver. I knew if I did my did my good vaults I could get in that top three," Ellie Downie said.
"I definitely wasn't expecting the silver on floor. I qualified in fourth and just wanted to go out and enjoy the last routine of the competition."
Fragapane also came fourth in vault, while Becky Downie was joint-sixth on beam and Gabby Jupp finished seventh on bars in her first international competition following a lengthy knee injury.
There was more British success at the European Gymnastics Championships in Bern as sisters Becky and Ellie Downie won gold and silver respectively.