There are pros and cons of this for both parties.
Will you undersell yourself to make yourself available more? I am assuming your parents had 1 stretch limousine. Was their single car fleet utilization 100%?
What you are suggesting cannot compete based on how much you charge. And you cannot think of earning more by taking on more customers as this will cause your latency to degrade.
You are looking at a customer segment that is willing to pay extra so they need not do it themselves. And you need to deliver quick.