Busch previously took on Sheeran in a $20 million copyright lawsuit over the superstar's song Photograph - ending in a settlement which earned the two suing songwriters music credits and a significant royalty share.
The lawsuit alleges the top-30 hit was copied from Australian Jasmine Rae 's 2014 hit, "When I Found You".
"He works directly with the Tim and Faith label team in Nashville", Rae allegedly wrote in an email to Carey and Golden, according to the lawsuit.
They're seeking at least US$5 million in damages and for a permanent injunction blocking the use of the song. The two were tipped off during a conference call with Tim Holland, a Sony marketing manager and the boyfriend of "When I Found You" co-writer Jasmine Rae.
Sheeran, along with co-writers Johnny McDaid, Steve Mac (real name Steve McCutcheon) and Amy Wadge and their respective publishing firms were named.
"The copying is, in many instances, verbatim, note-for-note copying of important and original elements of the Song, and is obvious to the ordinary observer", claims the lawsuit.
The legal action is being led by lawyer Richard Busch, who has become something of a trailblazer in this area, since successfully convincing a jury that Robin Thicke's "Blurred Lines" was a total rip-off of Marvin Gaye's "Got To Give It Up" in 2015.
But it's not just McGraw and Hill who are in trouble with Carey and Golden.
The lawsuit later states that when Holland was first asked about the similarities between the two songs, the Sony employee chose to remain silent on the matter to avoid any confrontation with his company. It's alleged that from there, other people within Sony provided the defendants - including Sheeran - with access to Rae's song. Though Rae is a co-writer on the tune, she's not a part of the suit.
"When pressed further by (Carey and Golden), Mr. Holland indicated that he had known that the songs were substantially similar for more than two months prior to the October 5, 2017 release date of ('The Rest of Our Life')", the suit says.
Holland is not named as a defendant in the suit, and Rae is not a plaintiff, though she and the plaintiffs are said to have enjoyed "excellent professional relationships and communication since the song's creation".
Carey and Golden also provide a second potential explanation for the supposed similarities: they state Sheeran was touring Australia at the peak of When I Found You's popularity and radio airplay. Sony, which represents McGraw and Hill, did not immediately respond to a request for comment.