14 drives connected externally. That would look like monstrosity.
And for plex server - storage drives have to be connected permanently. Removable connection is not good for such use.
And NAS to connect 14 drives, this is going to be expensive...probably not an option.
I think optimal way would be upgrade of your mini itx small case pc to
larger case with more space for storage drives,
(not all cases can support 14 drives, may need to add 2.5 drive backplane)
larger motherboard with more pcie slots,
couple of additional pcie sata controllers, because normally motherboards do not support 14 drives,
may be necessary to upgrade PSU too.
That way you could connect all those drives internally.
Or ... 2x of such external drive enclosures. This probably will be more expensive than pc upgrade.
https://www.raidsonic.de/products/external_cases/external_cases_35/index_en.php?we_objectID=5672