That would probably be possible however I don’t think it’s really the best idea. Depending on what language you use it might be a better idea to just pay a service to handle your storage. Usually, it’s very difficult to handle lots of storage and it’d be easier just to get a service like AWS S3. I was looking into this myself and I personally used S3. It’s got a very good API (for Go anyway).
If you mean paying a second VPS with another hosting package it’d be slower, harder to use and a lot more expensive. Mainly because you’d have to pay for an entire other CPU and RAM package that you won’t even use. Just paying for an extra HDD from S3 will only cost around $0.023 per GB each month.
Not to mention less work, you only need a DB storing file IDs and then just upload your file as bytes to the server and it’s done. Dealing with writing and reading is difficult especially as you get to a large scale.
Hope this helps.