List of remixes that add extra vocals to the track (not counting rap remixes)

On the double-disc "Everything is Wrong" remix album by Moby, the instrumental "Hymn" gets a remix with vocals.. a woman repeating "Because I believe in God.."

"Hymn" had some vocal samples when it was released as a single in 1994 (the "This Is My Dream" mix was the one they usually played on radio and MTV), but for some reason Moby didn't include that version on the Everything Is Wrong, rather than an instrumental piano version (which is based on the coda of the "European Mix" of "Hymn").

Sisa Mix of Something About You by Level 42 has a chant bit that qualifies for this thread.
Flesh And Blood version of The Word Girl by Scritti Politti has a totally different vocal, by Ranking Ann.
There must be some Pet Shop Boys ones - the Always On My Mind on Introspective?

the Always On My Mind on Introspective?

That was the first thing that popped into my head, but the thread title says no rap.

also, that's a completely different recording, not a remix.

Pet Shop Boys remixes for others have form for adding vocals though - Hallo Spaceboy for David Bowie, the PSB Maxi Mix of Sorry for Madonna

Razormaid are edits/bootlegs though

That's what I always thought too, but a couple of years ago I bought a Razormaid comp which included their remix of Telex's "Raised by Snakes", and it has normal vocals instead of the vocoderised vocals of the original version. So they must've had access to the original tapes for that one at least.

The 12" remix of 'La Femme Accident' by Orchestral Manoeuvres in the Dark has some extra vocals on there which aren't in the 7"/album version. Having said that, it sounds like the whole thing is re-sung to me.

Dreamtrak - Odyssey, Pt. 2 (A. G. Cook Remix)