You can absolutely display the number of orders a customer has placed using Shopify’s Order Printer app. The Order Printer template uses Liquid, and luckily, Shopify gives us access to some useful customer data within the order object.
To show the number of orders a customer has placed, you can use:
{% if customer %}
Total Orders by Customer: {{ customer.orders_count }}
{% else %}
Guest Checkout – No order history
{% endif %}
Where to put it:
Since you mentioned you want it under the order number and date, look for this section in your Order Printer template (or something similar):