W3 Trends offers a Quick Qoute app. The customer builds their cart like normal but instead of clicking the Check Out button in the cart, they click the Request A Quote button. They’ll then be taken to a new page where they can see the products they added to the cart and be able to submit the quote with their information. The store can then edit the quote (change the products name, price & quantity, as well as add or remove products to the order) and send the quote back to the customer. The customer can then view the quote and accept it where they will be taken to the checkout page to complete their order.
https://apps.shopify.com/request-quote-w3?utm_content=contextual&utm_medium=shopify&utm_source=admin
Heres a demo of the app: