No.
The above answer is somewhat wrong but remains right, as far as a quick web search has found.
Why is it somewhat wrong? Chinese checkers is a team sport involving more than two teams, if each player is assumed to have multiple personalities, and if a board game can be considered a sport.
Also according to the below link there is a soccer variant being played that uses three teams, called showupandplay soccer. But sadly, these teams are rotated, with only two teams on field at any one time, so this isn't a MASH-up that is supportive of three simultaneous teams onfield. But it is three team.
Finally, many computer games have multiple teams, and with a mental stretch, these could be considered sports, though more mental than traditional physical sports. Some of the teams are AI teams, some are real representing the actions of the humans controlling the team, examples of older earlier games that used multi-team approaches are populous and powermonger, both by Peter Molyneux at Bullfrog.
Can anyone improve on this, with examples of traditional outdoors or indoor team sports that have more than two teams competing on field, where the teams are larger than two players?
Click on the link below for more information.
If they are Canadian and a sports team - they can be any sport they want.
Football rugby and cricket or Motor sports field sports or water sports
yes.
Yes.
Any team that is playing against the team you root for.
There is no single team that represents the British Isles in any sport.
Thera are many sports teams in Poland, can you be more specific?
yes
yes delaware has a baseball team
What are the three main skills utilized in team handball
Ajax is probably the most famous sports team in Netherlands.
yes bull dogs