It sounds strange that a game would eat up all your hard drive's space? Is your C: drive partitioned? Maybe you just need to repartition or delete some files from C:. However, you can buy an external USB 3 1TB hard drive for around $60 and it will have good performance IF your laptop has USB 3.
My parents bought me a Laptop this year that is a mix of both a school laptop and a gaming one. When I started buying games on steam I started to run out of room on my hard drive. I was wondering how badly the a usb port would suffer if i played games from a external hard drive.

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