Beastie Boys - Intergalactic
Phish has already covered Sabotage, so this isn't too much of a stretch. This is the kind of cover to slip into a Say it to Me S.A.N.T.O.S. jam.
Sufjan Stevens - Impossible Soul
At 25 minutes this song has six different parts all waiting to be explored. Phish could play only part V and easily jam it out to 25 minutes alone. This would be an epic cover.
King Tuff - Eyes of the Muse
This opening riff sounds so familiar and seems like something Trey can run with. If any song I choose gets a regular spot in Phish's rotation, I hope it is this one.
Vengaboys - We like to Party! (The Vengabus)
This is obviously a Fishman tune. The rest of the band just jams while he sings. All I know is this will be a great dance party.
Goose - Yeti
Maybe if Phish covers them people will stop complaining. If there ever was a Goose song for Phish to cover it would be Yeti.