Do any of you use a payment installment plan system for your business?

Klarna They charge a fee only if a sale is made. Around 2% fee

you can charge the financing cost to the customer if they choose to split the payments. Even in retail, financing has about 6-12% interest, depending on the length though it's usually absorbed by the retailer.

you can set up recurring payments outside of the Shopify ecosystem with something like waveapps.com or stripe. It requires you to manually create the invoice/subscription, but you can put an end date and automatically bill a set amount until then

other services are Splitit and Split that give you the option to create installment plans for your shopper