Aerosmith are a band that has several links to Alice. Alice has commented on how their career in many ways mirrored his own. 4/5ths of the band appeared on 'Trash' and Alice and Joe Perry worked together before the 'Constrictor' album.

Do you have the Alice/Joe Perry stuff from the 'Welcome To My Nightmare II' project?
Yes, I have a tape of the 3 or so songs they did. Actually the Nightmare II stuff was done a little later when Alice started working with Kane. These songs wound up being Constrictor. Alice was working with Joe Perry right before he did 'Monster Dog' and the the songs were done with that in mind. I guess they ain't that good or they probably would have seen the light of day by now.
(Renfield, July 1995)

They recorded a few demos together. They were done potentially for 'Monster Dog' of all things! But Joe was real interested in becoming partners with Alice. Anyway, Steve Tyler found out about it and kinda freaked. He was afraid that if AC and Joe hooked up that would really be the end of Aerosmith. So even though they weren't speaking to one another, Tyler swallowed his pride and called Joe and the rest is history.
(Renfield, May 1996)

The Aerosmith Version (From Biography "Walk This Way"):

Joe Perry: "April 1984, nothing much was happaening except rumors......Then Tim (Collins, Joe's manager) got a call from Alice Cooper, who wanted me to help him write some songs for and album.  I went out to Arizona to meet with him."

Steven Tyler: "I called Tim one day trying to find out where Joe was.  'Well, he's working with Alice Cooper'  It was the first time I had the balls to call Joe Perry up with all this anger I had in me.  'How can you be f***in' be working with ALice?  YOU NEED TO BE HERE!!!!"

Tim Collins: " Tyler calls me: Mother******!  You're breaking my band up!!!  Why do you have Joe writing with Alice Cooper? A**hole-who the f**** are you!?
I said, "You're right.  If you were smart, you'd get on a plane today, move to Boston, and start rehearsing with Joe."