Anytime I have travelled with family I check all bags in under my name. As long as the total count is under our combined baggage allowance (wprst case ever was 3+2+2+stroller+parentsinlaw2+2), I have never had a problem with an agent checking them all in under my name with priority tags.

When travelling with a work companion, I can't imagine an agent would refuse to priority tag both person's bags if you are standing there checking in together...it's never happened to me.

Forgetting the tag altogether, that has happened a few times.