@elajenta 

Are there any other accounting systems that allow this?

Other accounting systems of the same class as QBO use 3rd party payment processors (eg Stripe, Paypal). If you want to stay with QBO, you can use 3rd party solutions as well.

For B2B, use Melio

https://affiliates.meliopayments.com/get-paid

For B2B and/or B2C, use Veem

https://get.veem.com/qb_online