Time and time again I am shit on by AP heavy teams...

...and I have no idea how the fuck to counter it. I don't understand what I can do as a support main to protect my team from 3 bursty AP carries. I rush a Locket but that's all I can do. I tell my team to stack MR but they can never get enough to stop combinations of 3+ Kass/Veig/Morg/Akali/Diana/Lulu/AP Malph/Blitz/Vel/Nid. Lulu's ult+shield, Morg's shield, Janna's shield...I never have enough to protect a single person on my team from these 6000+ damage combos. So what the hell can I do? Just hope my team stomps so they can be far enough to ahead to not die so easily? Dodge when I see 3+ mages on a team with CC? I'm beyond frustrated with being so powerless against these comps.