I too would like to be able to setup variable payment (not a donation) through a squarespace-based website. As it is the only way I know of is to use a PayPal account (or other third-party payment processor), create a payment page on the Squarespace-based website, and include a Pay Now button on that page. PayPal does have an option to accept variable payment, it's been a while, don't remember how hard it was to find that option, but I did find that option.
In this case, my client is a food based business and they would like to be able to accept payment for catering jobs directly through their Squarespace website.
I have submitted a feature request to Squarespace Support.