First of all I want to clarify one thing on your question that I believe it's not accurate: SaaS is a way to deliver technology (products) not a business model. The counter part of SaaS is on-premise or legacy, which is not a business model but how you deliver your product.
For example, Salesforce is SaaS and their business model is charging per seat or user. Zenefits is a SaaS model and they don't charge the user of the product but take a commission out of insurances. Our company, COMPAS, is SaaS and we charge a monthly fee on an annual contract.

Sorry I didn't answer your question directly but I believe it's more important to ask the right questions before you get the wrong answers.