Question: Do items of the same type have bonuses that additively stack?
Yes, with some notable exceptions:
1. The bonus is a "UNIQUE" bonus. For instance, the passive effect from Infinity Edge- Critical hits now deal 250% damage instead of 200% damage- does NOT stack. So if you somehow got the ~8k gold necessary to farm up two Infinity Edges, you would not have Critical hits deal 300% damage, they'd only deal 250% damage. However, you would still have the +160 Attack Damage and +50% Crit Strike that both Infinity Edges give.
2. A "UNIQUE" bonus that's transfered from an item with its own "UNIQUE" bonus. (this to my knowledge only applies to Manamune/Archangel Staff.
The Manamune and Archangel Staff are two items that are based off the same "base" item, the Tear of the Goddess. The Tear of the Goddess has a unique passive wherein it gives +4 mana each time an ability is used, and both the Manamune and Archangel Staff keep that passive. However, if you were to build both a Archangel Staff AND a Manamune, you would not gain +8 mana per ability used- the abilites are considered UNIQUE even though they're different items, because they're both built out of the Tear of the Goddess, which is similar to itself (obviously).
3. Items with slow effects only take the "highest" slow when computing your slow percentage. This to my knowledge only affects Phage/Trinity Force/Frozen Mallet (ed: this also applies to Bilgewalter Cutlass/Hextech Gunblade and Warden's Mail/Randuin's Omen). When an item with a slow percentage is built, if it builds into another item which also slows, and you have both items, only the item with the "highest" slow is considered the active slow. In other words, Phage has a 25% chance to slow for 30% for 3 seconds; it builds into Frozen Mallet, which has a 40% slow for 2.5 seconds; the Phage also builds into Trinity Force, which has a 25% chance to slow for 35% for 2.5 seconds. If you had all 3 items in your inventory, and were lucky enough to proc all three items on one hit, it would only take the "Frozen Mallet" slow as the "true" slow and slow the target only for 40% for 2.5 seconds (I'm not absolutely sure that's how Frozen Mallet and TriForce interact but am positive that's how Phage and TriForce and Phage and FM interact so I might be wrong)
4. Unique Auras are Unique and only apply to a champ once. So for instance, if I had an abyssal scepter it would apply it's -20 magic resist debuff to every enemy champ near it. Unique Auras do not stack, so getting any other abyssals on any other teammates would be a waste of gold.
HOWEVER, IN THE CASE OF POSITIVE AURAS: Positive Auras affect your own
team with their positive effects, and also do not stack. However, the "holder" of the aura item, whilst getting the buff themselves from the aura item, are not COUNTED as receiving the aura item for the purposes of determining uniqueness. This means that for AURA ITEM HOLDERS ONLY, they can "double stack" aura items with a teammate.
Me (Rent), AhiMahi, and Minerva are on a team together. I decide to get an Aegis of the Legion (+270 Health
+24 Magic Resistance
UNIQUE Aura: +12 Armor, +15 Magic Resist and +8 Attack Damage to nearby allied units. (1200 range)). I DO get the benefits of the Aura from my Aegis, so I effectively have 270 Health, 30 Armor, 39 MR, and 8 AD from the Aegis. AhiMahi and Minerva receive +12 Armor, +15 MR and +8 AD from my Aegis Buff when near me.
Me (Rent), AhiMahi, and Minerva are on a team together. Minerva AND I decide to get an Aegis of the Legion.
We BOTH get the passive Aegis Aura benefits, in ADDITION to our own unique Aura benefits. HOWEVER, we ALSO get the OTHER'S aura benefit from their Aegis because our own Aura item is not counted as unique for the purposes of "UNIQUE" aura calculation. So, in other words, when AhiMahi, Minerva and I are next to each other, Minerva and I both have the +12 Armor, +15 MR, and +8 AD Aura buff (for an effective +24 Armor, +30 MR, and +16 AD buff), whilst AhiMAhi only receives it once (for +12 Armor, +15 MR, and +8 AD)
Me (Rent), AhiMahi, and Minerva are on a team together. All three of us decide to get an Aegis of the Legion.
All three of us receive the passive Aegis Aura benefits, in addition to ONE AND ONLY ONE OTHER PERSON'S unique Aura benefits. (Think like, Rent gets the buff from both himself and AhiMahi, but not Minerva's. Ahi gets it from himself and Minerva, but not Rent's, and Minerva gets it from both himself and Rent, but not Ahi's.) This means all three of us have +24 Armor, +30 MR, and +16 AD when grouped together.
ED : forgot these, adding for completeness
5. Attack Speed stacks additively and caps at 2.5 attacks per second. This takes into effect any runes, masteries, buffs, abilities or Items you might have to hit that cap and any over it has no effect.
6. Tenacity's bonuses are unique in that it only counts the highest Tenacity bonus (but, since the three items besides Mercury Treads (Cloak and Dagger, Eleisa's Miracle, Moonflair Spellblade) all have the same Tenacity bonus of +25, this in effect means that the highest Tenacity you CAN have is +35, and that is from Mercury Treads.)
7. CDR's bonuses cap at 40% CDR. This takes into effect any runes, masteries, buffs, abilities or items you might have to hit that cap and any over it has no effect.
And i think that covers how unique buffs work goddamn that's a lot of words