This is a question that came up while brewing a pir and toothy EDH Deck. let's say I've got Pir, imaginative rascal and master biomancer on the field, and play a card like Nimbus swimmer that enters the battlefield with a number of +1/+1 counters. Do I get an extra counter from Pir for both Nimbus swimmer's original counters and the bonus counters from master biomancer, or do I only get one extra counter, as nimbus swimmer enters the battlefield with both his own counters and those from master biomancer all at once?
It is all a single event, and Pir adds only one extra counter to the total.
"[Something] enters the battlefield with N counters" is a form of replacement effect that modifies the event of just entering the battlefield.
614.1c. Effects that read "[This permanent] enters the battlefield with . . . ," "As [this permanent] enters the battlefield . . . ," or "[This permanent] enters the battlefield as . . . " are replacement effects.
614.1d. Continuous effects that read "[This permanent] enters the battlefield . . ." or "[Objects] enter the battlefield . . ." are replacement effects.
614.12. Some replacement effects modify how a permanent enters the battlefield. (See rules 614.1c-d.) (...)
So all three abilities are replacement effects, changing the same event. As it is only one event, each will apply only once.
616.1. If two or more replacement and/or prevention effects are attempting to modify the way an event affects an object or player, the affected object's controller (or its owner if it has no controller) or the affected player chooses one to apply, following the steps listed below.(...)
616.1e. Once the chosen effect has been applied, this process is repeated (taking into account only replacement or prevention effects that would now be applicable) until there are no more left to apply.
At first you have the event of Nimbus Swimmer entering the battlefield. Both Nimbus's own replacement and Biomancer's replacement are applicable to this event, so you choose one to apply first. Either one you choose, the other is still applicable, and now Pir's replacement can be applied too. So all three end up being applied, once each.
Let's start with Nimbus's effect. Nimbus is not entering with X counters on it. Now apply Pir's effect. Nimbus is entering with X+1 counters. Finally, apply Biomancer's effect. Nimbus is now entering with X + 1 + P (Biomancer's power) counters. Pir's effect already applied so it can't apply again.
In this particular case, the actual order doesn't change the end result. Any way your order them, Nimbus enters with a number of counters equal to X, plus Biomancer's power, plus 1.
"[Something] enters the battlefield with N counters" is a form of replacement effect that modifies the event of just entering the battlefield.
614.1c. Effects that read "[This permanent] enters the battlefield with . . . ," "As [this permanent] enters the battlefield . . . ," or "[This permanent] enters the battlefield as . . . " are replacement effects.
614.1d. Continuous effects that read "[This permanent] enters the battlefield . . ." or "[Objects] enter the battlefield . . ." are replacement effects.
614.12. Some replacement effects modify how a permanent enters the battlefield. (See rules 614.1c-d.) (...)
So all three abilities are replacement effects, changing the same event. As it is only one event, each will apply only once.
616.1. If two or more replacement and/or prevention effects are attempting to modify the way an event affects an object or player, the affected object's controller (or its owner if it has no controller) or the affected player chooses one to apply, following the steps listed below.(...)
616.1e. Once the chosen effect has been applied, this process is repeated (taking into account only replacement or prevention effects that would now be applicable) until there are no more left to apply.
At first you have the event of Nimbus Swimmer entering the battlefield. Both Nimbus's own replacement and Biomancer's replacement are applicable to this event, so you choose one to apply first. Either one you choose, the other is still applicable, and now Pir's replacement can be applied too. So all three end up being applied, once each.
Let's start with Nimbus's effect. Nimbus is not entering with X counters on it. Now apply Pir's effect. Nimbus is entering with X+1 counters. Finally, apply Biomancer's effect. Nimbus is now entering with X + 1 + P (Biomancer's power) counters. Pir's effect already applied so it can't apply again.
In this particular case, the actual order doesn't change the end result. Any way your order them, Nimbus enters with a number of counters equal to X, plus Biomancer's power, plus 1.