Her other two items are flexible, ideally you want Kraken's Fury and Death Blade.
Caitlyn's ult can already crit, so she doesn't need Infinity Edge, but it's okay on her, same with Last Whisper and Striker's Flail.
Catilyn can do very well with Double Kraken's Fury or Double Death Blade. So don't hesitate to take augments which give you extra bow and sword!
Augments such as Deadlier Blades, Sword Overflow, Speedy Double Kill are the best to provide Catilyn items.
For Sivir
Sivir is the 2nd carry, if your Caitlyn started with Crit items, you can eventually move those items to Sivir. This is because Crit items on Caitlyn later on become a overkill, Caitlyn will waste a lot of damage if she builds crit items.
Because Sivir is a Caster, she will also need one mana generation item, it can be either Blue Buff or Spear of Shojin.
Sivir BIS: Infinity Edge + Blue Buff + Last Whisper
For Elise
Elise is your main tank, therefore you want best tank items on her.
Gargoyle Stoneplate provides a lot of resistance, especially in the early game when you can solo-front Elise.
Warmog's Armor provides the health on top of the resistance.
Crownguard is considered the best tank item right now.
Rakan can shield himself while providing a huge attack speed boost to Caitlyn, so he is really the secret sauce for this comp.
The best item for Rakan is Protector's Vow.
This item will allow Rakan to start casting much faster and make Caitlyn a beast.
Use Coven Cashout for Quicker Elise and Caitlyn 3 stars
During the mid game, play a 3 Coven board to gain stacks, and cashout only at 85-130 stacks.
This is because this gives the best chance for you to 3 star Elise quickly and gain more components.
How to Roll/Leveling
Level to 6 at 3-2, and roll for the Coven board above.
Stop after you hit 2 stars Elise and Caitlyn.
Try to 3 star Caitlyn and Elise before 4-1.
Then start to level up.
Rakan is also very good to 3 star if you are close, but don't have to.
After you reach Level 8,
Try to roll for the 4/5 costs Vanguard --- Sentinel and Taric. Use them to replace the 3-costs vanguards Diana and Hecarim.
Add in Sivir. If you find Ashe, it's even better, remember to itemize Ashe if you happen to find her, Ashe is extremely useful even at 1 star.
Add in Vi for 2 Juggernaut and 2 Primal, for the Primal Blessing, choose the "Blessing of the Turtle" for more tankyness.
That's the whole guide. This comp is extremely intuitive and smooth to play with, I hope you enjoyed, and please check out our tierlist to have a more completed picture of the meta, it will help improve your gameplay. <3