Hey ourjoyfullife,
You absolutely can using QB merchant services as ZackE mentioned, but there is also an easy option if you'd prefer to use your own merchant account. Bill & Pay has a payment plan feature that you can setup, or even enable as an option for customers to set. Payments are processed through your merchant account and synced with invoices automatically.
https://www.billandpay.com/payments.php
Anyone who would like to see this in action can reply here or contact me at telsenbaumer(at)axiapayments(dot)com.
