According to the Law of Surprise in Netflix's The Witcher series, a person bound by the same has to give his saviour something that he has and is not aware of. What if the person has more than one thing which he is not aware of? Is he supposed to give all of them?
The Law of Surprise refers to the first thing.
In the book The Last Wish, Mousesack narrates a story to Calanthe and the others that clearly explains the Law of Surprise. Here is the snippet from the book:
"As you command, your Majesty. Noble Calanthe and you, knights! Indeed, Urcheon of Erlenwald made a strange request of King Roegner, a strange reward to demand when the king offered him his wish. But let us not pretend we've never heard of such requests, of the Law of Surprise, as old as humanity itself. Of the price a man who saves another can demand, of the granting of a seemingly impossible wish. 'You will give me the first thing that comes to greet you.' It might be a dog, you'll say, a halberdier at the gate, even a mother-in-law impatient to holler at her son-in-law when he returns home. Or: 'You’ll give me what you find at home yet don't expect.' After a long journey, honorable gentlemen, and an unexpected return, this could be a lover in the wife's bed. But sometimes it's a child. A child marked out by destiny."
—The Last Wish, page 138
Thus, in case you find two things that you didn't expect after getting back home, the Law of Surprise holds for the first among the two that you witness when you gt back home. And it is highly unlikely that you will see all the unexpected things at the same time.
Addition: Just for the sake of an example, suppose that after being asked by someone for the Law of Surprise, you return home and find two things that actually were unexpected: your wife got a new TV, and also find your long lost brother waiting for you in the living room. Which one would you see first? The brother of course. So you get to keep the telly but lose your brother by the Law of Surprise.