Beast Ball supply - am I cheesing it?

So I've just gotten to where

Looker

gives me missions, and I noticed his dialogue says that I still have Beast Balls. Great. So I wondered what happens if I don't have any, so I put all of them on PC-stored Pokémon.

He gave me another. I repeated the process of hiding it. I got another.

Is there a limit to this? Or will there be a way to get more later on and I'm just being overly cheap hoarding them one by one now?

You can receive an unlimited number of extra Beast Balls, one at a time, from Looker. This is the only way to get extra Beast Balls in the post game.

The "limit" on the number you can physically have at the same time is the number of Pokemon that it is possible to store in your party and PC. Assuming 31 boxes of 30 Pokemon + 6 Battle Box + 6 for party + 1 extra, you've got a limit of 943 Beast Balls at once.