How many leases can one person be on at one time? Maximum amount.

As many as they can afford. There is no legal limit that I ever heard of but for each lease signed they will be responsible for the rental. There may be a limit within an apartment complex though. A landlord may not allow someone to lease more than one unit.

Why do you ask?

Some complexes may have rules that they allow, but you can have all you want and can afford. When I traveled to several states on regular basis I had 5 apartments rented.
So the reasons you want them rented. If you were going to have two just a mile from each other, the landlords may want to know why.