In 2001, Hirt proposed a receipt-free voting scheme, which prevents malicious voters from proving to anybody how they voted, under the assumption of the availability of a helping server that is trusted for receipt-freeness, and only for that property.  This appealing design led to a number of subsequent works that made this approach non-interactive and more efficient. Still, in all of these works, receipt-freeness depends on the honesty of one single server. In order to remove this single point of failure, we design a new model in which multiple helping servers are available and propose a new security definition called threshold receipt-freeness. Our definition requires that receipt-freeness should be guaranteed even if some of the helping servers happen to be fully malicious and ensures that voters can express their votes even if the corrupted servers choose the content of their local view of the ballots. Eventually, we propose a generic construction of a single-pass verifiable voting system achieving threshold receipt freenes with a mixnet-based tallying process. Our ballot submission process relies on the recently designed traceable receipt-free encryption primitive.