The problem is that when teamfights start with blitz your importance diminishes, you're still supposed to be peeling for your carries as best as you can, but that ability is minimal.
Blitz isn't really a team fighting support to be honest. His importance and usefulness is before the teamfight, when people are dancing back and forth like idiots, you want to grab someone and pull them out of position to make the fight a 4v5 to give your team an edge, since let's face it, you're not much of a presence in a team fight.
What you can contribute to team fights is aura items. So look to buy things like Locket of the Iron Solari, or a Banner of Command, you can pick up Frozen Heart, buy a Zeke's which now isn't an aura, but still helps your ADC, or whatever carry you put it on.
There's a lot of options for items to build on him, just make sure you don't waste CDR. I'm also a huge fan of switching from Targon's Brace/Face of the Mountain over to Talisman of Ascension late game. As much of a gimmicky item as people think it is, I'm a pretty big fan of ZZ'Rot portal on Blitz, just because blitz doesn't have a ton of useful items to build without going over the CDR cap, so this way he gets some tankiness, and can give some siege power since base turrets are so hard to crack sometimes.