Split invoice to same recipient

Is it possible to split an invoice to the same recipient? Or how would the following scenario be possible?

After the intake I propose a psychodiagnostic investigation consisting of for eg. 7 different appointments over the course of lets say 10 weeks. The appointments vary in length and with that varies the cost of each appointment. Clients are required to pay 50% of the total amount before the first appointment and the remaining 50% of the total amount before the last appointment. I noticed that when I split the invoice, the splitted invoice must be someone else than the recipient of the created invoice.

I used to create separate invoices for each appointment, but would prefer to create one invoice containing all the appointments for that psychodiagnostic investigation, and split it so when I receive the first payment I can enter that payment to the first 50% and and assign the second half of the invoice and payment date to a later date.