Claudia Fragapane, Becky Downie and Sam Oldham all won silver for Great Britain on the last day of the European Gymnastics Championships in Montpellier.
GB finished with a best ever tally of eight medals at a Europeans.
Downie enjoyed success on the beam before Oldham and Fragapane followed on high bar and floor respectively.
"Just to come in the top three is incredible. I'm overwhelmed," Fragapane told BBC Sport.
"The next goal is the Worlds. We want to get a really good team result and if there are individual results, even better."
Fragapane, in her fourth final of the championships, was in the gold-medal position before being pipped to the top prize by 0.1 points by the last competitor, Ksenia Afanaseva of Russia.
The four-time Commonwealth champion was also fourth in the beam competition.
The previous best GB medal total in an individual European Championships was five in both 2009 and 2013, while their best European Team Championships was in 2010 with seven medals.
Downie's silver was her second of the event after she made the podium in Saturday's uneven bars final.
"It's really exciting ahead of the World Championships in October but I don't think we should relax," she said.
"We'll take the positives but we'll also look at what we did wrong and where we can step it up."
Oldham's success came on his return to international competition after suffering a serious ankle injury at the Commonwealth Games in Glasgow.
"It's been about the journey for me and to come away with a medal is more than I could have hoped for," said Oldham.
"To have made the Europeans that was the main thing - especially after I was lying in my room eight months ago, injured, not know knowing what was going to happen."
Having won floor gold on Saturday, Kristian Thomas could only manage fifth in the vault and sixth in the high bar, while 15-year-old Amy Tinkler was sixth on the floor.
The other GB gymnasts to win medals in Montpellier were Louis Smith with gold in the pommel horse, and Ellie Downie and Dan Purvis who both won bronze in the all-around.