I would say by definition South Carolina unilaterally seceded from the country known as the USA. When the next state Mississippi seceded it was no longer "unilateral" secession.
All states must participate in the decision or else it is unilateral.
Unilateral is defines as "(of an action or decision) performed by or affecting only one person, group, or country involved in a particular situation, without the agreement of another or the others."
One state or ten, their actions were taken without discussion or agreement of the other side. It was unilateral.