Have a variety of capacity vehicles, including full sized buses. Have bus stops and have people indicate where they are going, and set preferences (like "willing to accept a change for a discount" to allow better vehicle utilisation), and dynamically adjust the routes accordingly and use minibuses or smaller cars to "backfill" capacity to aim to guarantee that you can be picked up within a certain time.
Having fixed routes and scale up size of vehicles based on actual detailed drivership data would be very interesting.
I know from my own bus usage that having the certainty that there'll be a bus "soon enough" makes a big difference in how often I take the bus vs. when I'll order a car. If I know that if I go to the bus stop I'll get one or the other but guaranteed within a short time, it'd remove most of my need for ordering cars.
Yes, if you're driving alone, you have to use a single car. But having the car take care of finding others going (effectively) the same place, and picking them up seamlessly, for only a short increase in commuter time (and a corresponding drop in fare), will make these cars do a whole lot more than 2-4 trips a day.
In fact, given how much of a difference in arrival time for the people on my project (anywhere from 6:30 am to noon to 1pm) I think the cars will be able to do quite a few trips.