I'm not aware of any limits on the drive capacity.
Price is a factor to consider, since the 4TB SSD drives that fit (2.5 inches) are not cheap. How much are you willing to spend on upgrading this machine?
Have you tried using an external HDD for media storage? For me that's the sweet spot for flexibility and affordability. I can copy a bunch of files over to the internal drive when I want them and then delete them to make room for others later. The 2010 mini only has USB 2.0, so I wouldn't use an external for startup, but for me it works fine for data storage.
Also curious, do you use the optical (CD/DVD) drive? If not, you might want to consider the relative cost of getting a used 2012 mini, which would be much more powerful and could accommodate 2 internal SSDs.