The Outfield - Everytime You Cry?
UPDATE: I went through and listened to snippets of all the songs on the list I didn’t know. None of them were the song in question. I’m beginning to think that it’s a song I actually do hear and know well, but I’m just not making the connection with the “make it sweet more” thing.
This was from the 70s, and is probably played a lot, so I doubt this is the song, but it’s not My Sweet Lord by George Harrison is it?