Has it ever happened in the Olympic history that 3 members of the same family will take part at the same edition of Olympic games (both winter and summer editions)? What is the record for the most family members?
The record for the most siblings in the same Olympic Games is 4. This happened when the four brothers Luis Adrián, Jorge, José and Roberto Tamés from Mexico competed as two 2-man bobsleigh teams at the 1988 Calgary Winter Games. See 1, 2, 3.
Three siblings competing in one Olympic Games has happened several times:
Summer Olympics, 3 siblings
- Americans Edward, Richard and William Tritschler competed in gymnastics at 1904 Saint Louis Olympic Games.
- Japanese brothers Kazuhito and Yusuke Tanaka won silver medal in London 2012 as a member of Japanese gymnastics team. They also competed in individual competition. Their sister Rie Tanaka competed at the same olympics in both team and individual
- Steven, Mark, and Diana López represented USA at several Olympic Games. In 2008 Beijing all three of them won a medal. See also: 1, 2. 3
- The Estonian triplets Lily, Leila and Liina Luik competed in marathon at 2016 Rio Olympics. (They were mentioned already in the question.)
Winter Olympics, 3 siblings
- The sisters Thérèse, Anne-Marie and Marguerite Leduc competed in women's slalom at 1960 Squaw Valley.
- The brothers Marcos Luis, Martín Tomás, Matías José Jerman from Argentina competed in cross-country skiing in 1976 Innsbruck.
- The brothers Peter, Marián and Anton Štastný played for Czechoslovakia in 1980 Lake Placid. Czechoslovakia ended up 5th in the tournament.
- In 2014 Sochi the Canadians Justine and Chloé Dufour-Lapointe won gold and silver medals in women's moguls, while the third sister Maxime finished twelve.
- The sisters Aita, Selina And Elisa Gasparin competed in biathlon in 2014 Sochi. Selina Gasparin won silver medal.
Another example of four siblings in the same Olympics is the Belgian Borlée family during the 2016 Rio olympics.
The brothers Jonathan, Kevin and Dylan participated in the 4x400m relay, taking fourth in the final and missing the medals by three hundreds of a second. Jonathan and Kevin also ran individually in the 400m event, while Jonathan added the individual 200m to that. Jonathan and Kevin are twins, while Dylan is the younger brother.
They have an older sister Olivia, who participated in the 200m event in Rio. She was part of the team that won the 4x100m in the 2008 Beijing Olympics after a recent disqualification for doping of the Russian team that finished first.
Their father, Jacques Borlée, is the coach and participated himself in 1980 Moscow Olympics.
Three brothers Charles,Ned and Paul McIlroy competed on the United States Olympic Water polo team in 1964. The brothers graduated from El Segundo High School, in El Segundo, California. Paul graduated in 1955, Charles in 1956 and Ned in 1958.
There were also the four Pettersson brothers of SWEDEN who competed as one team for the Team Trial, Cycling event in Mexico 1968 Olympics. The four, Erik, Gosta, Sture and Tomas, also won the silver medal in that event.