How many mortgages can I have on my credit?
You can have as many mortgages as you want on your credit. There's nothing that says that you can't borrow as much money as you are qualified for to buy real estate. The trick, however, is finding a lender that will play ball with you.
If you are looking for a conventional/conforming loan, the new guidelines provide that you can have no more than four financed properties. So, what you'd need to find is a portfolio lender that does not impose limits on the number of financed properties for people seeking new loans.
If you have good credit and are willing to establish a business banking relationship, a local bank is probably the way to go. There used to be several wholesale lenders who would lend to people with up to 10 or 20 financed properties, but they have eliminated the programs which allowed that.