No, one per, as in one loyalty counter per damage it would do. So if it's a 2/1, it would do 2 damage, remove 2 loyalty counters, add 2 poison counters, add 2 -1/-1 counters, etc.
In that example, that creature would deal 3 damage to you and your damage would be applied in the form of 4 -1/-1 counters to the attacking creature. After the damage step, that creature would be sent to the graveyard as a state-based effect from the poison counters, whereas if regular damage kills a creature (instead of reducing it's toughness with counters, it causes damage) it goes to the graveyard immediately. This is important because the attacking player can play an instant that gives it +1/+1 counters (or something like giant growth to counteract it) before it is sent to the graveyard but after damage is applied, whereas regular damage doesn't afford that opportunity.