Ok short answer he can only get two but buffing all 3 gives he too much versatility since all of them ornn likes and wants to build so you end up in a situation where ornm can build for anything.
Long answer
No he can only get two but still it makes him much more versatile then he should be since those item do basically everything now for ornn so if you go into a game thinking ill build those 3 items first it gives him a lot of room as to how you want to itemization since mask already gives enough mr for most teams with one mage without the upgrade so you can build that 3rd since you want it to increase your damage but if that one mage is a problem then you can very easily go for it 2nd and it will give basically two full mr items worth of mr and it's the same with armor since he can go into a game thinking I can get iceborn for trading and then go into sunfire for the health and the damage or mask for the mr. You want sunfire to be built with mask since it helps out the damage by a good bit but in the early game and mid game the build path and the damage is much better if you go into iceborn first.
Ornn after this buff will basically only have 3 choices for items for his first 3 items and all the items give him everything he needs and the ones that get upgraded can make him very hard to kill especially vs full ad teams.