Can You Log In 3 Controllers to One Xbox Live Account in Black Ops?

No. It is technically impossible.

1 Xbox Live Account = 1 Active Session. You cannot sign in the same Microsoft Account on multiple controllers simultaneously on one console.
1 Controller = 1 Signed-In Profile. Each controller slot (1–4) maps to a different profile (Guest or full Account).
Black Ops (and all CoDs) enforce this: Split-screen multiplayer requires each player to have their own Xbox Live Gold / Game Pass Core subscription (on 360/One/Series) to join online matchmaking. Guest accounts can only play local split-screen (offline / custom games with host).

Scenario	Requirement	Online Matchmaking?
1 Player	1 Account + Gold	Yes
2 Players (Split-Screen)	2 Accounts + 2 Gold Subs	Yes (most CoDs)
3 Players (Split-Screen)	3 Accounts + 3 Gold Subs	Yes (BO1/BO2/BO3 support 3-4 player split online)
4 Players (Split-Screen)	4 Accounts + 4 Gold Subs	Yes (BO3, BO4, WWII, Vanguard, MWII/III)
Guests (No Gold)	Host Account + Gold + Guests	NO. Local only (Custom Games, Bots, Campaign).

Each player needs their own account + subscription for online play. No shortcuts.

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