It is "then we raised a glass to JFK and a dozen more beside" (links below)
Do you native speakers understand "1 glass/drink to him plus to 12 other people" or "1 glass to him plus 12 more glasses/drinks", or is it actually ambiguous?
The original version of that song is from the Pogues (I don't link to it because it's so hard to look at). Anyway my favourite interpretation is this one: