Obviously, all four Beatles never again recorded anything together after the Abbey Road sessions in 1969. So for the purposes of this mix, the limitations for choosing songs are for things recorded from Lennon's last creative output (for the Double Fantasy sessions in 1980) up to the year 1989, which was when Paul McCartney's above average (for him) Flowers in the Dirt was released. That album contains a couple of songs I can definitely imagine The Beatles recording, as I will explain.
So between 1980 and 1989, this would include, from John, Double Fantasy and the posthumously released Milk and Honey (recorded late August 1980, released in 1983). From Paul, McCartney II (released in mid-1980), Tug of War (1982), Pipes of Peace (1983), Press to Play (1986), and Flowers in the Dirt (1989). For material from which to possibly select songs, I'd exclude McCartney's movie soundtrack, Give My Regards to Broad Street (1984), which except for a favorite of mine, "No More Lonely Nights," was simply re-recordings of Beatles compositions, and СНОВА Б СССР (1988), essentially McCartney's version of Lennon's Rock 'n' Roll. From George, Somewhere in England (1981), Gone Troppo (1982), Cloud Nine (1987), and Traveling Wilburys Vol. 1 (1988). From Ringo.......well, er, I'll pretend the Fabs politely considered putting "Stop and Smell the Roses" (from his 1981 release Stop and Smell the Roses) on this imaginary album as the perfunctory one-per-album Ringo song, and then wisely decided against it.
This then, perhaps, might have been the album they'd have released in 1989, which I'd call Everest (or maybe A Doll's House?):
"My Brave Face"
Also, I like to believe the lyric "Now I don't have to tell anybody when I'm gonna get back" is a reference to "Get Back." I think McCartney's expression at 1:16 in the video confirms my belief. "My Brave Face" sounds like a deliberate attempt by McCartney (and Costello) to be Beatlesque, right down to the first reappearance (the video for "Coming Up," notwithstanding) since the Beatle days of his Hofner bass (complete with Candlestick Park play list, still taped to it). Anyway, it could have been a pretty decent opening song to the first "real" Beatles album in twenty years...
"Nobody Told Me"
Strange days, indeed.
"Tug of War"
"What opportunities did we allow to flow by
Feeling like the timing wasn't quite right?
What kind of magic might have worked if we had stayed calm..."
No longer riding on the merry-go-round-hound!
I can clearly remember hearing this on the radio in those days after Lennon's death, back in December 1980.
The recording of the song featured all three remaining Beatles (Harrison, Starr and Paul McCartney), though this was expressly a Harrison single. It is one of only a few non-Beatles songs to feature three members of the group. Harrison and Starr recorded the song at Harrison's Friar Park studios between 19 November 1980 and 25 November 1980. After Lennon's death the following month, Harrison removed Starr's vocals (but left Starr's drumming track) and recorded his own vocals with rewritten lyrics honouring Lennon. McCartney, his wife Linda and their Wings bandmate Denny Laine visited Friar Park to record backing vocals. (source)