An average game only sees ~11,000 gold per player and lasts ~33 minutes.
Factor in 1k for boots, and 1k in the bank when the Nexus is exploding, and you're only looking at an average of three 3k gold items.
It's also worth noting several unique passives/actives that offer the power spike you grab a certain item for aren't even provided until the item is complete, which often pushes the unique qualities of your 3rd major item so far into the game you only get to use it for ~1 team-fight, win or loose, before someone's Nexus explodes.
So - any build with more than 3 major items isn't particularly useful to create.
It's significantly more important setting up the first 3 items.
Placing them in a specific build order is also quite important.
You should never have Muramana in an item slot past the 2nd item slot, as it's completed power spike will likely never happen, and that spike is massive. It also takes 11 minutes and 7 seconds to get max stacks and transform under optimal conditions (assuming you never die, never run out of mana, and never run out of abilities to cast). So - 2nd item is pushing it, as you likely won't have the massive spike until you complete your 3rd major item, which will only apply to about 1 fight. With Muramana as the 1st purchase, you can hit a monster power-spike around the time you complete your 2nd major item and late game just starts.
You probably want RoA as your first major item, and no later than the 2nd major item. With 10 minutes of a charge-up time, you logically want it at least 10 minutes before the game's over - and with three 3k items in 33 minutes, that's 1st or 2nd.
Archangel's spike is mostly from completing the item itself for the mana to AP, the stacking effect isn't that important, but with RoA and Muramana - you probably shouldn't have it with RoA and Muramana.