From my perspective, an objection is a tension. So I'd follow the "One person, one tension at a time" rule and integrate the valid objections one by one under the "standard".
I wouldn't coach the circle members to not raise an objection that has already been raised. The objection might be different regarding the role sensing the tension... and if the tension is the "same", it will drop with the previous integration.
Even non valid, objections might give information to the circle, so it would be a loss not to take advantage of them. (That's my thought, in any event).