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

Doors can be golden, upgrading the tier of the connected room when opened.

Rooms contain an object that opens all locked doors.

Rooms contain Vaal Vessels.

Rooms contain Gold Piles.

Rooms contain Cursed Treasures which drop stacks of currency when claimed, but reduce remaining Incursion time.

Rooms contain a Vaal Flesh Merchant.