The victim, a 35-year-old transient, had been stabbed in the rib cage and upper back. He was taken to the hospital in critical condition, but was in serious condition Wednesday after being stabilized.
Another fight about an hour earlier, at 210 S. Rio Grande, also initially left a man hospitalized in critical condition, but he, too, was upgraded after being stabilized.
McGowan said the bleeding 27-year-old victim had walked into a homeless shelter suffering a wound to the lower back.
"He stated he had been in a fight and felt something stick him," McGowan said.
There was no description of the suspect in that case.
The third stabbing occurred just before noon Tuesday when two brothers got into a fight at 130 E. 2nd Ave. That incident ended with one of them, a 44-year-old man, also hospitalized in critical condition, but he had improved to serious-to-fair condition as of Wednesday. Police responding to a 911 call arrested the victim's 42-year-old sibling and booked him into the Salt Lake County jail on suspicion of aggravated assault.
Anyone with information on the suspects still at large is asked to call Salt Lake City police at 801-799-3000.