Currently the space limitation of where the SATA drive fits is whats holding you back. Presently thats a 2 TB drive (HD or SSD). If and when a larger 2.5" drive which is no bigger than 9.5 mm in height comes onto the market then it maybe possible.
As to the number of drives your system can support it can support one SATA drive and one PCIe blade SSD (limit of two drives internally).
Migrating to a larger drive will require a SATA to USB adapter cable or a Thunderbolt HD case to house your new drive to transfer the data to and then swapping out the drives.
Frankly, I would recommend going with an external Thunderbolt RAID drive system. Here you can get a much larger drive configuration (as an example 8 or 10 TB) and gain the speed of the Thunderbolt connection which is faster than the internal SATA III (6.0 Gb/s) interface.
As to upgrading your system with a SSD: You'll need to install the needed cable assembly as your system currently does not have it. You can see it here in the IFIXIT teardown: Mac Mini Late 2014 Teardown in Step 9 in addition to the custom Apple SSD unit.
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