Limit Orders Per Customer

We are looking to limit the number of orders that can be placed by a given customer to prevent trying to work around per-cart limits (using the Woocommerce Cart Limit plugin) by placing multiple orders. We have started forcing account creation to place an order, but everything I’ve found to impose additional limits seems to be geared toward limiting numbers of individual products, not of total products. Thanks in advance for any suggestions on how we can accomplish this.