Its impossible to have a set build for any game if you're a support. Just the way it is. However, situationally certain things seem better.
Leona is incredibly strong, there is no reason to abandon her. I would suggest getting eye of the equinox rather than ruby/mountain. It gives you space for more items. This is personal preference and not necessarily a need. If your carry needs a shield and you're good at putting it on them, then by all means build them separately. Gj on the awareness of locket. I hate building it since its a squishy tank item, but it really helps your team. I wouldn't make it core if the enemy is mostly ad though. (maybe just the support and the jungle do ap damage)
What boots do you normally run? If you've dominated early, I like mobi's. If the enemy has a double (triple???) ADC comp, ninja tabi is GREAT. Swifties if they've got slows for days. The usual.
I run strength of the ages on her. This gives me more health without having to build it. I know its not the most popular choice, but its nice to have that little beef.
Bashee's vs Spirit: If you're initiating and they have good cc, I like banshee's more. If you're playing the peel game, I prefer spirit visage. Get both if their only ad is the adc. (unless the adc is the only one fed, but even then)
I love deadman. Mmm, that speed up and the proc on leo? Beautiful. Randuin's? Are you paying attention to the enemy when you buy this? There are a lot of things with armor, this is best if they have Yas, Tryn, maybe Cait/Jinx for the crits. You only really want it if the enemy is getting lots of crits. Frozen heart is good vs jinx, cait, ashe, jhin even. You lower the attack speed (which lowers jhins damage). Thornmail is only really my go to if the adc is stupid fed or if the enemy team is high auto attack ad. Warmogs is RARE. That's basically me saying, I'ma be spoiled this game and buy me this baby. A health item with armor or mr would be a better substitute.
Lets talk Zz'Rot. Its great. Gives you resistances to both sides. Annnnd it gives you the one thing you never get as a support: wave control. It also helps you seige turrets.
Sunfire cape is another good armor item and good if you're diving constantly, just don't stack sunfire with mobis. (I've done it by accident so many times)
Iceborn guantlets are fun too, but that's also a I'ma be spoiled item. Great if your team needs a little extra cc atop all the cc you already give.
So basically....you can build anything :D but you need to be aware of what the enemy team is, what they are building, and who's getting fed. What's going to be an issue late game, who's coming up on a power spike, what does my team need to help protect them better. Support is a mother, and it doesn't matter what tank you pick, its the same story every time.
Btw: all support tanks are squishy unless you get fed in lane. You have the least gold so its hard to keep up in items to stay ahead of the carries.