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Each time you cast a spell, every source you have that has extort triggers. When each trigger resolves, you can pay W/B or not. If you pay, each opponent loses 1 life and you gain life equal to that lost. If you don't pay, it does nothing. If there are more triggers waiting to resolve, you move to the next.
To answer your question, Each Extort ability is a separate trigger. Similarly to how Elvish Archdruid 's triggered ability will only trigger once when it enters the battlefield, your one extort creature, lets say Syndic of Tithes , will only trigger once when you cast a spell. Since the trigger allows you to pay W/B or not, it doesn't allow you to do it any number of times. You will only be ble to drain your opponent 1 life.
The above posters are correct but let me create a scenario to show you how it will work. If you have 1 Syndic of Tithes and 1 Blind Obedience on the battlefield and 4 untapped Plains and you tap one of your plains to cast Boros Elite you may pay to activate extort a total of twice. Once for Syndic of Tithes and once for Blind Obedience . Assuming you are playing against a single opponent they would lose a total of two life and you would gain a total of two life. At this point you would have one Plains left untapped but no more extort triggers to pay for.
Hope that helps.
Each permanent with Extort must be paid for seperately and can only be done once for each trigger (ex. If you cast a single spell with 3 Extort permanents on the field, you can then pay for it up to 3 times).
Just to make sure it's clear, each instance of Extort triggers on each spell "cast" This means that even if the spell is countered, you can still proc extort. It will also proc off of the new Cipher effect since the wording has you choosing to cast the copy of the spell.