Damage bonuses (including from ABM) do not change the character's base damage stat.
For example, an OR Recruit (10dmg) who hits someone while ABM is active will hit for 20 dmg (10 + 10). If that Recruit is within 6 of a Czerka Scientist, then she'd have Twin attack, for a possible 40 dmg (20dmg twice).
SAs that specify a new Damage rating (like Poisoned Blade, except the attack becomes a melee attack) actually change the character's base damage rating, and so when they were active they would prevent a 10dmg shooter from gaining Twin from the Czerka (because the shooter is now a 20dmg shooter)...that character would instead now gain Jolt instead (via Blaster Rifle Upgrade).
The same applies to the OR Senator's CE: it does not change the character's base damage stat, but it just adds more damage to the total.
_________________ "Try not! Do, or do not. Thereisnotry." --Yoda
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