recurring invoice - how to have overdue balances show on the next invoice, like any utility bill

I am currently charging customers on a payment plan a fixed amount every month. I do this using a recurring invoice, so that in January, February, etc. they receive invoices for the monthly amount. Let's say it's $1000.

This works great when people pay on time. But sometimes they miss a payment and then things get confusing, as they get automatic reminders for each payment they miss as well as invoices for the new monthly installment. Thus, if they miss the February payment, they will receive an email for the march payment of $1000 and, a couple of days later, a reminder for the missed February payment. If they miss two payments they can be getting three or more emailed invoices or reminders in a single week, each for $1000.

When I get a utility bill (or any bill) this is all consolidated. If I miss my February payment, the missed amount is reflected on my March bill. No matter what, there is only one current invoice, and it reflects everything. Can I make this happen for my clients? If they miss an invoice payment ($1000) in February, I'd like for them to automatically receive an invoice for $2000 in March, rather than a reminder for the February missed invoice (of $1000) and a new March invoice ($1000). Bonus points if it could automatically add a late fee.

Is this possible? How?