Are you flying on DL or KE equipment? Makes a huge difference,
KE will honor your Plat status, but not the Amex card.
As far as companions, that gets veery messy and I have no idea what really works. On DL there is really no such thig as adding pax as "companions". You just have to do it with a human at the airport. You can have some agent "link: their tickets to yours, but that means little.
To make matters worse, I just checked a recent "international" flight (I am not sure if LIR is international in DL speak), and I only see one free bag allowed for me. I am also PM and Amex. I assume this is just part of the game played by airlines to game the DOT regs. In short, I do not think DL will give you legit answers on bags.
If you are on KE equipment you need to talk with them.
If you are on DL equipment they will take 3 bags of yours. I think (but do not know) the companions just have to be with you at check-in to get whatever benefit they are entitled to.