At least one Modifier will always apply when spending Threads. Spending more Threads improves the chances of multiple Modifiers applying.
Betrayal Modifiers which can be applied by Threads:

Catarina will accompany a Syndicate Encounter in the Area.

Dealing with downed Syndicate members will apply powerful Buffs to all Players and Mercenaries in the Area.

Catarina's Corpse Sculpture will appear somewhere in the Area.

Syndicate Members will have an additional Rare Monster modifier.

Veiled Items dropped in Area will have their Veiled Modifier Fractured.

Area will contain many additional clusters of barrels and chests from Syndicate Safehouses.