It's his version of Vincent McHugh's
Caleb Catlum's America (1936) -- all the characters he liked are all working together. McHugh had the characters from American fable being all part of the same family, immortal, sexually active, comically sprightly. In the end they were all driven out by the faceless bad guys, "The Traders".
Right after the McHugh book came out, it became Heinlein's touchstone for friendship, if you didn't like the book, he didn't want to have anything to do with you. When he got to where he could write what he liked, he did the same thing.
But Philip José Farmer had managed to get it out first with his "Wold Newton" universe, where all the characters
he liked from pulp and adventure fiction were all members of the same family, descended from the members of an excursion hosted by Sir Percy and Lady Blakeney who happened to get too close to a radioactive meteor. (Farmer didn't seem to be aware that Baroness Orczy wrote fifteen more books in the series, including one set in the nineteen-twenties with a great-grandson of Percy and Marguerite.)
Farmer's key relationship was that Tarzan and Doc Savage were first cousins. He wrote fictional biographies of them (
Tarzan Alive (1972) and
Doc Savage: His Apocalyptic Life (1973)) and a bizarre three book series about two people who are them under different names, of which the first is grossly pornographic (
A Feast Unknown (1969)) and the second and third aren't (
Lord of the Trees and
The Mad Goblin (1970)) and end on an unresolved cliffhanger to boot.
Farmer had to do gross violence to the continuities of the various stories, had a somewhat muddled idea of the British honours system, and as I said, for all that the Blakeneys were supposedly the prime movers in this, their direct descendants don't figure in the story. Worse yet, Farmer fans have extended this; I sort of gave up when I heard that Peter Parker (as in Spider-Man) was a "Wold Newton" descendant. (I suppose a Spider-Man fan will chime in on how great Spidey is. See above about continuity.)
Heinlein didn't have to worry about continuity, because his "Circle of Ouroboros" could time-travel as well as travel between time-lines. As a result, for example, he managed to undo one of the few moving scenes in
Methuselah's Children, where Lazarus Long is remembering how much it hurt when his mother died, by first having him become his mother's lover, then saving her life.
Again, as all the characters in Farmer's "Wold Newton" works become Farmer characters, whatever their personalities had been in the original stories, thus all the characters in the "Circle of Ouroboros" stories become Heinlein characters. It doesn't work when young fanboys (or really fangirls) write about Captain Kirk falling in love with Ensign Mary Sue (or Mr. Spock), much less when a writer of skill and experience does it.