At my gym, we do offer either “pay in full” package (5, 10, or 20 sessions) or the optional “financing” PT package. The “pay in full” is just that, the member has to pay for the full amount of PT sessions up front…which is expensive to most. With this option, they can use the sessions whenever they like. The other “financing” type of package, does give the member the option to choose however many sessions they would like to attend (5, 10, 20) and then break it down even further into sessions they want to dedicate themselves to on a weekly basis (1, 2, 3, 4, 5). Each week, the member is then automatically charged based on the amount of weekly sessions they committed to whether they attend the session or not. I designed software for my billing company that allows for weekly billing.
I would definitely be interested in learning more about the specifics of your model.