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

All rewards offered by the Ultimatum Encounter will be Inscribed Ultimatums.

All rewards offered by the Ultimatum Encounter will be Catalysts.

The Ultimatum Encounter will lead to the Trialmaster.

The Ultimatum Encounter will spawn a beating heart every round. Defeating this heart will grant Adrenaline to all players and mercenaries in the area for a duration.

The Ultimatum Encounter will allow you to Double Down at round 7 or 8.

The Ultimatum Encounter will spawn Cursed Currency every round, which can be claimed. Claiming it will add random Currency rewards to your collected rewards so far.

The Ultimatum Encounter will spawn with a nearby Soul Core. Claiming the Soul Core will cause all Ultimatum Encounter types to complete more quickly, but can empower Ultimatum Enemies.

The Ultimatum Encounter will offer secondary upsides for each round alongside the usual difficulty Modifiers.