What determines the initial damage multiplier of a chain attack?

There are many things that affect the base damage modifier for Chain Attacks, and this GameFaqs guide breaks it all down.

When starting a Chain Attack, the absolute base modifier is a static percentage according to your difficulty settings. For most difficulties, the base modifier is 300% except for Bringer of Chaos where the base modifier is reduced to 150%¹.

The base modifier can further be increased by unlocking affinity nodes for Rex and Morag. In Rex's standard affinity chart, unlocking the Tier 3 "Ultimate Relay" will increase the base modifier by 50%. Morag's "Golden Opportunity" can only be unlocked in the Tier 3 Hidden Affinity during a New Game+. By using these two characters with their unlocked affinities, the base modifier can be increased to 400% (250% in BoC).

An accessory that also affects the base modifier is the Burst Symbol. The Burst Symbol can increase the base modifier by 100%, 150%, and 200% for the common, rare, and legendary versions respectively. By equipping a legendary version to each driver, this will effectively increase the base modifier by an additional 600%.

Finally, which the guide I linked mentions it is unclear how it is calculated, performing various tasks such as combat arts, special attacks, and general damage output will further increase the damage modifier.

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¹ According to the Wiki, there is a bug that will reduce the base modifier from 150% to 100% after performing any Cancel attack. It does not say one way or another if this bug has been resolved.