Using the Arcane Archer as an example, say you have a Ranger 8 / Sorcerer 3 multiclassed character and, upon reaching the next level, you decide to become an Arcane Archer.
At level 8, a ranger can do two attacks per round. The BAB for the Arcane Archer (all the way to level 10) only references one BAB value. Does this mean that the PC can only use one attack if he/she wants to use their arcane archer abilities or does this BAB add to the bonus of the Ranger class at its current level?
nope, doesn't mean that at all, your number of iterative attacks is a function of your total BAB. (see page 11 of the core rule book)
I believe they're only additive meaning you get the Arcane Archer bonus to the to the first attack only.
EDIT: Totally misunderstood the question, obviously. As was said, the full amount of your BABs across all levels are in effect at all times.
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Regardless of whether you're adding levels of base classes or prestige classes, your BAB from different classes stacks.
So from your 8 levels of ranger, you have +8 BAB. From your 3 levels of sorcerer, you have +1 BAB. Each level of Arcane Archer gives you +1 BAB.
So when you hit level 12 and take your first AA level, your BAB goes from +9 (8 ranger plus 1 sorcerer) to +10 (adding the 1 from AA).
Same for base save bonuses.
Using the Arcane Archer as an example, say you have a Ranger 8 / Sorcerer 3 multiclassed character and, upon reaching the next level, you decide to become an Arcane Archer.
At level 8, a ranger can do two attacks per round. The BAB for the Arcane Archer (all the way to level 10) only references one BAB value. Does this mean that the PC can only use one attack if he/she wants to use their arcane archer abilities or does this BAB add to the bonus of the Ranger class at its current level?
When you take the first level of Arcane Archer your BAB increases by 1. Take your existing BAB, and add 1 to that value. That is now your BAB.
Same thing for Saves. Take your old Fort, then add 1. Reflex, add 1. Will stays the same (+0)
If you had 8 levels of ranger (BAB +8/+3) and three levels of sorcerer (BAB +1) you would be character level 11, with a BAB of +9/+4. At character level 12 you take one level of Arcane Archer, your BAB becomes +10/+5.
When you take a second level of Arcane Archer (at Character Level 13) your BAB would become +11/+6/+1 and you would have three standard attacks in a full attack. (Not including Two-Weapon Fighting, rapid shot, haste, or any other method of getting more attacks)
They would stack together from my understanding. Ranger BAB +8, Sorc BAB +1. So next level you will have a BAB of +10 and a full attack of +10/+5.
Great. Thanks guys!