Police said they were called to 800 W North Temple around 12:15 a.m. Friday.
When officers arrived, they found a man with a gunshot wound. That victim was taken to a hospital in critical condition.
Later, police learned of another person who suffered several stab wounds in the same incident. The stabbing victim drove himself to a hospital and is in serious condition.
Police talked with a third person who ran from the scene.
"There was a man that was running away. Officers went and located him, found him. He probably is a witness and knows what's going on, but we're not getting a straight story," said Lt. Dave Cracroft, SLCPD.
Police said they took a fourth person into custody for questioning and they're still working to determine a motive.