There are even cases of three charting simultaneously with the same song, and a few cases of four and one (at least) of five!

Here is one of the fives...

Love Is A Many Splendoured Thing (1955) by The Four Aces / Don Cornell / David Rose / Woody Herman / Don Dick & Jimmy

Here are two of the fours....

Love Is Blue (1968) by Paul Mauriat / Al Martino / Claudine Longet / Manny Kellem
Kansas City (1959) by Wilbert Harrison / Rocky Olson / Hank Ballard / Little Richard

Here are a few of the threes....

Stranger On The Shore (1962) by Akcer Bilk, The Drifters and Andy Williams.
Alley Oop (1960) by Dante & The Evergreens / Hollywood Argyles / Dyna- Sores
Almost Paradise (1957) by Norman Petty Trio / Roger Williams / Lou Stein
Proud Mary (1969) by Checkmates Ltd / Creedence Clearwater Revival / Solomon Burke
White Silver Sands (1957) by Don Rondo / Owen Bradley / Dave Gardner
No Arms Can Ever Hold You (1957) by Georgie Shaw / Pat Boone / The Gaylords
Theme From Love Story (1971) by Andy Williams / Francis Lai / Henry Mancini
Seventeen (1955) by Fontane Sisters / Boyd Bennett / Rusty Draper
Seven Days (1956) by Dorothy Collins / Crew Cuts / Clyde McPhatter
Ode To Billy Joe (1967) by Bobby Gentry / Kingpins / Ray Bryant

Here are a fraction of the twos....

Heartbreak Hotel (1956) by Elvis Presley / Stan Freberg
Blue Suede Shoes (1956) by Elvis Presley / Carl Perkins
A House Is Not A Home (1964) by Dionne Warwick / Brook Benton
I'm Walking (1957) by Fats Domino / Ricky Nelson
Last Kiss (1974) by J Frank Wilson / Wednesday
Early In The Morning" (1958) by Buddy Holly / Rinky Dinks (actually Bobby Darin)
Abraham Martin & John (1969) by The Miracles / Moms Mobley
Ain't That A Shame (1955) by Pat Boone / Fats Domino
Tutti Frutti (1956) by Pat Boone / Little Richard
Long Tall Sally (1956) by Pat Boone / Little Richard
Alfie (1966) by Cilla Black / Cher
Wheels (1961) by The Stringalongs / Billy Vaughn