How can I qualify to giveaway more games at once?

I believe that leveling will grant more GA slots.

For giveaways completed with feedback from the winner will give you a extra giveaway slot. Deleting any giveaways will lose you a slot so be careful. Once your two giveaways complete and feedback has been given, it will give you more slots. You can also ask support for extra giveaway slots but they will usually need a reason for it.

Taken from the FAQ.

Why is there a limit to the number of gifts I'm able to give away?
We limit the number of gifts a user can create for security purposes, and to prevent a new user from potentially posting a large number of invalid gifts to the site. When you create giveaways and your gifts are received, this number will increase. At that time you'll be able to create giveaways with a greater number of copies, and more simultaneous giveaways.

You get one addition slot for 3 giveaways that you have done and successfully completed, where the winner marked the game received.

Every time you need to delete a giveaway, that results in a loss of a slot, same thing if you have a giveaway that's marked not received.

I don't think there's a maximum number of slots, you can just keep accumulating them as far as I know. There are plenty of people who have given away thousands of games, I imagine they have 4 digits in terms of slots. (I have 700 completed giveaways, I have 236 slots, with one outstanding giveaway waiting to be marked for completion, so I guess I really have 237.)

If you want more slots to use temporarily to give away a number of games, you can always ask support to give you some extra slots. I did that when I started, and I got maybe 20-30 extra slots. They were only given to me one time, I used them and then my stats reset back to what they were, but with those, I was able to accumulate enough additional slots to not feel like I didn't have enough.

You create giveaways and winners mark them as received. That's how you get more giveaway slots. You can get quite a few of them over time: " You're able to create up to 601 additional gifts based on your giveaway feedback." < that's what it says for me.