He's so good at that. I know Presidents started replacing the final line of Lump with that of Gump, I wouldn't be surprised if other bands do similar things. Of course that's a parody, not a pastiche, but still.
Last time I was on a road trip, the 10-minute-long "Stuck In The Drive-Thru" came up on my stream and about halfway through, my daughter in the back seat goes "Who is this?!? It's epic!" I think she's been hooked on Weird Al ever since?
A fair number of the original artists have been outlasted by Al, but I deeply wish we could get an album of them covering Weird Al's style covers. I think TMBG would be up for it, and I suspect you could get Trent Reznor to cover "Germs."
"Mission Statement" off of Mandatory Fun is totally a style parody of Crosby, Stills, and Nash. Pretty funny too, because it takes the sound of a free love hippie group from the 60's and uses it to ramble off a bunch of corporate buzz words.
I could see it being a straight parody of their song "Carry On", but Al usually sticks a lot closer to the original arrangement when doing song parodies.