Yes, you can get more than one, but not through the storyline. Like RecreativeReshiram said, there is a chance that a secret pal will give one to you. Or you could try to win one from the Lotto ID on the first floor of the Lilycove Department store.
To get one from a secret pal, they must have the special skill 'Pick something up'. When you get them to use it, there is a chance that they will give you a master ball. But if they don't, you have to wait until tomorrow until they can do it again. To make it easier, get the maximum amount of secret pals, and make sure that they all have the special skill 'pick something up'.
To get one from the lotto ID, the only way you can get good prizes without insane luck is by getting loads of Pokemon from different people. This is because they decide what you win by choosing a random 5-digit number, and seeing how well it compares to the ID numbers of all your Pokemon. If all the digits they chose match the ID of one of your Pokemon exactly, you get a master ball. But you must trade loads, because every Pokemon you catch has the same ID, and so will everyone elses. So catch lots of Pokemon and put them all on wonder trade if you want to do it this way.
But both these are still really unlikely to get you a master ball, so you could always trade an un-used one from another game in gen 6.
Sources: http://serebii.net/omegarubyalphasapphire/supersecretbases.shtml and http://serebii.net/omegarubyalphasapphire/dailyevent.shtml