If they do an encore together - which would only make sense, because if they have no shared encore, the first band would be perceived as simply "opening" - then I was wondering what songs they could do. Here are some that came to mind:
Eagles songs
Take It Easy - a natural for an encore, the Eagles have arranged this for multiple singers before (check out
Take It Easy with Linda Ronstadt and Jackson Browne)
Heartache Tonight - they all could harmonize on the verses, Glenn Frey on lead vocal otherwise. Its fun, party feel would be great for the gang all hanging out on stage together.
Take It to the Limit - my fave Eagles song with Stevie and Lindsey on it - oh my gosh! Alternating verses with Glenn Frey and Lindsey. It's not as if Glenn originated the vocal anyway, so it's up for grabs to share, I say!
Life in the Fast Lane - applies to the Mac too certainly! Alternating leads on verses between Don Henley and Stevie. Joe Walsh and Lindsey could share lead guitar parts.
Witchy Woman - what a hoot to have Stevie dancing around as Don and Lindsey trade vocals about the woman who will "rock you in the nighttime 'til your skin turns red." It would be too cool (yeah, I know it's not ORIGINALLY about Stevie but it would be tons of fun to apply it to her). Heck, maybe Joe Walsh could even do a verse. He can relate, too...
Seven Bridges Road - for those unfamiliar with this song, it's straight-up multiple harmony throughout. It would be magnificent. Check it out
here.
Fleetwood Mac songs
Don't Stop - Instead of Stevie and Lindsey sharing the lead, it could be shared with Lindsey and perhaps Glenn Frey. I'd love to hear the Eagles and Fleetwood Mac all singing "oooooh.... don't you look back..." Joe and Lindsey could share lead guitar duties.
Say You Love Me - Lindsey has already re-arranged this song to be a song that features multiple harmonies and alternating leads. Just throw the Eagles into the mix! Stevie, Lindsey, and Don Henley could each do a verse.
Farmer's Daughter - I don't really like this song, but the layered harmony leads throughout would work. They haven't done it since 1980, though, so it would be a challenge.
Of course, they can throw in some covers and do whatever the heck they want, like Stevie did with Don during their encores for the Two Voices tour.
I think the possibilities are very exciting, and I will be very disappointed if they don't take advantage of the opportunity to perform at least a couple songs together.