It is actually pretty easy to figure out what songs could have been on the Beatles next album, simply by looking at the solo work and songs that came out immediately after their acrimonious breakup in 1970.
The biggest surprise of this album though would be the fact that John and Paul would have probably played a lesser role in the songwriting department, as George had been stockpiling a number of heavyweight tunes that had previously been denied a place on a Beatles record.
But that all changed during the recording and subsequent release of their final studio album, Abbey Road. The first single was Here Comes The Sun, followed by one of the greatest love songs ever written (so says Frank Sinatra-and who's going to argue with him), Something.
It was during these sessions that the band also experimented with a prophetic, beautiful tune called All Things Must Pass. Anyone who's heard the Beatles version would probably agree that this song would have been a standout tune, especially with the lovely vocal harmonizing between George and Paul during the chorus. Unfortunately their relationship was strained to the point that the last thing George wanted to hear was Paul singing alongside him.
Another surprise on this album would be the inclusion of other non-Beatles participating in its making, which they had done previously on Let It Be (Billy Preston) and the White Album (Eric Clapton). With all the interpersonal tensions in the band, the members actually enjoyed having "neutral" players break the ice so that everyone could actually have fun and enjoy themselves again. It was kind of like a marriage that had soured, and sometimes having friends over for drinks and a BBQ is all that is needed.
So in saying that, I would speculate that Bob Dylan would guest on this album and offer a tune he gave to George for his first solo album. If Not For You is a mellow love song that would be a "new country" tune today, but I think it would have been amazing to see Dylan guesting on the next album of a band that simply idolized him years before, and which he influenced greatly (remember Rubber Soul).
Paul had a few songs that had been bumped from earlier albums, but which would finally surface on this latest album. The tunes Junk and Teddy Boy had both been written in India, but were cut from Abbey Road and Let It Be respectively, but with a little reworking they would make it on this new album, along with a classic. Maybe I'm Amazed was the stand-out track on McCartney's first solo release, and the Beatles version would have been far superior with the participation of the other quality musicians and the production of George Martin to do it justice.
Ringo's contribution would be a song that was his first solo release, and which many speculated was actually written by George or John due to it's level of songwriting. It Don't Come Easy was a number one hit for Ringo, and there's no doubt the Beatles version would have done equally well or better.
John Lennon was the most dominant member of the Beatles up until Sgt. Peppers, and then a number of factors precipitated his decline as leader. Meeting Yoko, experimenting with heroin, and losing Brian Epstein all affected John's feelings towards being a Beatle, and it was he (and not Paul) who first requested the dissolution of the band in 1969.
After the break-up, many people were shocked at a lack of quality Lennon material, as it would take him over a year to produce anything comparable to Beatles calibre, with the release of the song Imagine. Perhaps Instant Karma and Working Class Hero, which were a couple of solo songs released in 69/70, could have been offered to and put out on a new Beatles project, which would have guaranteed quality production and effort.
Of course the one song that would definitely be on this album, and which would also be its title, is the anti-war anthem Give Peace A Chance. This song sums up the passion and emotion of the man and the group as a whole, and would be reflective of the entire generation that grew up loving the Beatles, their music, and their message of love and peace.
Give Peace A Chance, the next album by the greatest musical group in the entire world. The Beatles.