Thank you for explaining what you are looking for.

I have changed the request summary to reflect what you explain in more detail in the comments.

Right now in gnucash, a partial payment can be applied to an invoice. However, it is simply shown as "not paid" in the "find invoice" dialogue box. There is no indication that any payment has been applied to the invoice.
This could be accomplished with additional columns showing original balance and outstanding balance.

Please explain a bit more what you are suggesting here: What can you do in GnuCash right now? What would you like to do instead, i.e. in what dialog window do you want to see another possibility to click or enter or whatever, and what exactly? Thanks.