Casey made a big point today (in 1979) that with the rise of the Pointer Sisters' "Fire" into the top 5, that was the first time three different songs with the same title had accomplished that, following the Ohio Players and Arthur Brown. This is distinguished from remakes of the same song, like "The Loco-Motion" which hit #1 twice plus a third top 5. In the last 40 years, no other "Fire"'s have gone that high, but...
Using my music catalog, I found some new matches with three trips to the top 5:
"Girlfriend" (*NSync, Pebbles, Avril Lavigne)
"Hero" (Mariah Carey, Enrique Iglesias, Chad Kroeger)
"If" (Bread, Perry Como, Janet Jackson)
"Jump" (Kris Kross, Van Halen, and Pointer Sisters)
"Power of Love (Kuther Vandross, Huey Lewis, and Celine Dion)
and one with four!
"Angel" (Aerosmith, Madonna, Shaggy, and Sarah MacLachlan)
You may have thought of "Hold On" which hit big twice in the 90's, but the many other songs with that title (including four top 40 entries from 1979-1982, all different), all fell short of even the top 10.
In October 1988, "Don't Be Cruel" made the top 10 concurrently by Cheap Trick (remaking Elvis) and Bobby Brown (new song)!
Later, both Robyn and Robin S. (confusing?) hit the top 10 in the 90's with very different "Show Me Love"'s.
The most unusual example could think of was when Tony! Toni! Toné! hit the top 40 with "It Never Rains in Southern California" which unbelievably was not a remake of the Albert Hammond classic.