'Stay With Me' Lawsuit -- Random Guy Wants Money and a Grammy!

A random guy claims Sam Smith stole his hit song "Stay with Me" right out from under him, but using the guy's logic, he ripped off The Supremes.

Mark Halper claims in a new lawsuit ... he cut a demo in 1986 of a song called "Don't Throw Our Love Away." He says it begins with the "phraseology and significant phrase, 'stay with me.'"

Ergo ... Halper believes Sam Smith -- who uses the phrase "stay with me" 8 times in his hit -- has ripped him off.

So how's this for a little music history. In 1964, The Supremes recorded their massive hit, "Baby Love." In the song, Diana Ross, Mary Wilson and Florence Ballard repeatedly sing, "don't throw our love away." Therefore, The Supremes own Mark Halper.

As for Halper's lawsuit, he's not going after Smith. He's suing several record labels. Among the things he wants ... a recommendation to the National Academy of Recording Arts and Sciences to acknowledge him with a Grammy.