We suggest you create an item in the Store with an open-ended price by selecting Add Price at Checkout when you create the Product. Do not check the box to allow this Product to appear in your Online Store and Cashier Store, but do Enable Pay Later. Then, when you send an invoice from Accounting > Pay Later, you will add the $ amount before you Add to Cart and assign to the student. This method will allow them to pay in full online or send in a check for full or partial payment. It will not allow an automatic payment plan since it is built for you to add the $ amount later. Here is an example:

https://bh.boosterhub.com/store/1870/4329

If you need to allow the Payment Plan option, you would create items with each specific $ amount.