Clapton also soloed on the Beatles “While My Guitar Gently Weeps” written by George Harrison…
…as mentioned in the OP (initial post of this thread). 
I’d say it depends on how strictly we define “member.” If I remember correctly, the band had already recorded three or four of the tracks for the album before Duane came in as Eric’s invited guest. Duane’s arrival made an immediate and profound impact, and he blended into the sessions seamlessly. But when the album was finished, and D&TD went on tour promoting it, Duane joined them on stage for only two of those concerts.
In my opinion Duane was the star of that album (to nobody else’s detriment), and when he was in the studio with them he was effectively a member whether or not he was technically a guest.
If this counts, Kirsty MacColl’s singing on the Pogue’s Fairy Tale of New York:
Ellen Foley’s vocal on “Paradise by the Dashboard Light.”
And to those of us who remember the 1980s, Ellen Foley (although she did other acting and singing jobs) is mostly memorable as that woman who played the public defender one year on the TV program Night Court.
Mark Knopfler on the Dylan album Slow Train Coming
And Mark Knopfler on the Joan Armatrading album The Shouting Stage.
We could really derail this thread and mention session players who laid down amazing solos on many tracks, first and foremost for me would be the aforementioned Skydog Allman on Wilson Pickett’s “Hey Jude”…
Then there is the Steve Hunter/Dick Wagner combo on so many songs, playing for Lou Reed and Alice Cooper (although they were considered members of the band), but Aerosmith, "Train Kept A Rollin"...And finally, Matt Guitar Murphy and Steve Cropper both of whom played as house band members for various record labels before becoming famous as part of the SNL NRFPTP band and the Blues Brothers…
Some great responses to this thread. (Kudos especially to whoever pointed out Steve Winwood’s fantastic playing on “Voodoo Chile.”) My adds:
David Mason’s piccolo trumpet on “Penny Lane”
Nicky Hopkins’ keyboards on “Revolution” (the fast version)
Mark Knopfler on Dylan’s “Blind Willie McTell”
Ronnie Scott, saxophone on “Lady Madonna”
John Sebastian (of the Lovin’ Spoonful) played the harmonica on “Roadhouse Blues” when Jim Morrison couldn’t cut it himself.
Rumor has long had it that that’s Pete Townshend playing the solo on the Stones’ “Sway,” but I’ve never heard it confirmed. Sounds more like Mick Taylor to me.
No, that’s definitely Taylor, sounds nothing like Pete Townshend (never heard about that rumor before). If it was true, it would shatter my notion of it being my favorite Mick Taylor solo and favorite solo in general.
I think it got it wrong; turns out the rumor is that Townshend provided backing vocals. That’s more like it.
That happened to me with regards to Taxman and my favorite “Harrison” guitar work.
Ok, I wouldn’t totally count that out, but I only hear Keith on backing vocals.
ETA: great song by the way. One of my favorite deep cuts by the Stones.
When Weird Al Yankovic did his parody of “Money for Nothing”, that’s Mark Knopfler playing the guitar.