Did any group perform at Monterey Pop Festival, Woodstock and Altamont?

Yes. Jefferson Airplane, for one.

https://en.wikipedia.org/wiki/Jefferson_Airplane

Santana

http://books.google.com/books?id=ofF24d-a0KQC&pg=PA67&lpg=PA67
http://woodstock.wikia.com/wiki/Santana

Here's the June 17, 1967 concert listing on the Who site:

http://tinyurl.com/3dt3ffh

And Santana wasn't at Monterey Pop:

https://en.wikipedia.org/wiki/Monterey_Pop_Festival#Performers

Crosby Stills and Nash were at Monterey as Buffalo Springfield and at the other two as Crosby, Stills, Nash and Young.
https://en.wikipedia.org/wiki/Monterey_Pop_Festival
https://en.wikipedia.org/wiki/Altamont_Free_Concert
https://en.wikipedia.org/wiki/Woodstock

As I posted before, Crosby and Stills played at all three together. No Nash and no Young, though. At the time of Monterey, the Springfield were Stephen Stills, Richie Furay, Dewey Martin, Bruce Palmer, Doug Hastings (hiding in the shadows next to Palmer on the linked video) and David Crosby.

http://www.youtube.com/watch?v=doZVQA-Rrkw

https://en.wikipedia.org/wiki/Buffalo_Springfield

"Although Palmer returned to the group at the beginning of June, Young had already left and as a result missed the celebrated Monterey Pop Festival, at which the band performed with former Daily Flash and future Rhinoceros member Doug Hastings on guitar and guest David Crosby."

So, to summarize:

1) Jefferson Airplane played at all three.
2) Crosby and Stills played together at all three, but as two different groups with different members (Buffalo Springfield and CSN&Y).
3) The Grateful Dead was supposed to play at all three, but the Dead canceled during Altamont because of the violence during the Airplane's set.
4) Santana played with the Who on the same weekend as Monterey Pop, but Santana was not at Monterey Pop, although they were at the other two.

And that's it, because the only other two acts at Altamont were the Rolling Stones and the Flying Burrito Brothers. Chris Hillman of the Burritos played at Monterey with The Byrds but not at Woodstock, and the Stones weren't at either.

If you want two showing, Joe MacDonald of Country Joe and the Fish played two of them, Woodstock and Monterey.