three-way 
adjective
Involving three directions, processes, or participants: a three-way race for the presidency a three-way switch...
- This season we have had eight different drivers winning races and a three-way title fight up to the penultimate round.
- John is part of a three-way race for an open U.S. Senate seat in Louisiana.
- In 1924, the British team won gold after a three-way play-off for the Olympic title with France and Sweden.