How many games have you downloaded on your Switch at once? I think my grand total sits at two, so I'm not really pushing the system's limits. Believe it or not, there is indeed a limit as to how many games you can grab from the eShop at one time. Reddit user Nme84 put together a test, and he found out that users can download 64 games at once. I'm not sure why you'd need to download that many at once, but now you know!