Prestashop allows customization of products before purchase by default. The feature is a bit rudimentary, since it basically offers two field types to be enabled for a product, text and file upload ones, but in most cases it's pretty much enough because there’s no limit in how much of them can you enable.
The PRO version of the quote module recognizes them by default and, once they are filled, saves and displays them, both on the quote overview page and on the quotes history details page.
Of course, when creating a new quote, the admin also has the option to fill in these fields and add the product to the process, similarly to the creating of a new order in back office.
The icing on the cake
In catalog mode, Prestashop removes customization fields together with the purchase options, but the quote module detects their presence and displays them, and does this in a more user-friendly way than the default Prestashop. So both the client and the shop owner have the opportunity to see and use them even in catalog mode!